diff --git a/OpenTelemetry.sln b/OpenTelemetry.sln
index 4808898d5e4..9b3439cb449 100644
--- a/OpenTelemetry.sln
+++ b/OpenTelemetry.sln
@@ -144,7 +144,7 @@ Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "OpenTelemetry.Instrumentati
 EndProject
 Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "OpenTelemetry.Instrumentation.Http", "src\OpenTelemetry.Instrumentation.Http\OpenTelemetry.Instrumentation.Http.csproj", "{412C64D1-43D6-4E4C-8AD8-E20E63B415BD}"
 EndProject
-Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "OpenTelemetry.Instrumentation.Grpc", "src\OpenTelemetry.Instrumentation.Grpc\OpenTelemetry.Instrumentation.Grpc.csproj", "{0246BFC4-8AAF-45E1-A127-DB43D6E345BB}"
+Project("{9A19103F-16F7-4668-BE54-9A1E7A4F7556}") = "OpenTelemetry.Instrumentation.GrpcNetClient", "src\OpenTelemetry.Instrumentation.GrpcNetClient\OpenTelemetry.Instrumentation.GrpcNetClient.csproj", "{0246BFC4-8AAF-45E1-A127-DB43D6E345BB}"
 EndProject
 Project("{2150E333-8FDC-42A3-9474-1A3956D46DE8}") = "docs", "docs", "{7C87CAF9-79D7-4C26-9FFB-F3F1FB6911F1}"
 EndProject
diff --git a/README.md b/README.md
index 391b4c560bd..77f2ebde197 100644
--- a/README.md
+++ b/README.md
@@ -31,7 +31,7 @@ libraries](https://github.com/open-telemetry/opentelemetry-specification/blob/ma
 
 * [ASP.NET](./src/OpenTelemetry.Instrumentation.AspNet/README.md)
 * [ASP.NET Core](./src/OpenTelemetry.Instrumentation.AspNetCore/README.md)
-* [gRPC](./src/OpenTelemetry.Instrumentation.Grpc/README.md)
+* [Grpc.Net.Client](./src/OpenTelemetry.Instrumentation.GrpcNetClient/README.md)
 * [HTTP](./src/OpenTelemetry.Instrumentation.Http/README.md)
 * [Redis client](./src/OpenTelemetry.Instrumentation.StackExchangeRedis/README.md)
 * [SQL client](./src/OpenTelemetry.Instrumentation.SqlClient/README.md)
diff --git a/src/OpenTelemetry.Instrumentation.AspNetCore/Implementation/HttpInListener.cs b/src/OpenTelemetry.Instrumentation.AspNetCore/Implementation/HttpInListener.cs
index d13e97e9578..505349c6671 100644
--- a/src/OpenTelemetry.Instrumentation.AspNetCore/Implementation/HttpInListener.cs
+++ b/src/OpenTelemetry.Instrumentation.AspNetCore/Implementation/HttpInListener.cs
@@ -22,7 +22,7 @@
 using Microsoft.AspNetCore.Http;
 using Microsoft.AspNetCore.Http.Features;
 using OpenTelemetry.Context.Propagation;
-using OpenTelemetry.Instrumentation.Grpc;
+using OpenTelemetry.Instrumentation.GrpcNetClient;
 using OpenTelemetry.Trace;
 
 namespace OpenTelemetry.Instrumentation.AspNetCore.Implementation
diff --git a/src/OpenTelemetry.Instrumentation.AspNetCore/OpenTelemetry.Instrumentation.AspNetCore.csproj b/src/OpenTelemetry.Instrumentation.AspNetCore/OpenTelemetry.Instrumentation.AspNetCore.csproj
index 6dac8e7872a..86c0d4f0dc1 100644
--- a/src/OpenTelemetry.Instrumentation.AspNetCore/OpenTelemetry.Instrumentation.AspNetCore.csproj
+++ b/src/OpenTelemetry.Instrumentation.AspNetCore/OpenTelemetry.Instrumentation.AspNetCore.csproj
@@ -7,7 +7,7 @@
 
   <ItemGroup>
     <Compile Include="$(RepoRoot)\src\OpenTelemetry.Api\Trace\SemanticConventions.cs" />
-    <Compile Include="$(RepoRoot)\src\OpenTelemetry.Instrumentation.Grpc\GrpcTagHelper.cs" />
+    <Compile Include="$(RepoRoot)\src\OpenTelemetry.Instrumentation.GrpcNetClient\GrpcTagHelper.cs" />
   </ItemGroup>
 
   <ItemGroup>
diff --git a/src/OpenTelemetry.Instrumentation.AspNetCore/README.md b/src/OpenTelemetry.Instrumentation.AspNetCore/README.md
index 7f65261e918..aff0d720d35 100644
--- a/src/OpenTelemetry.Instrumentation.AspNetCore/README.md
+++ b/src/OpenTelemetry.Instrumentation.AspNetCore/README.md
@@ -5,6 +5,8 @@
 
 Automatically instruments the incoming requests to [ASP.NET
 Core](https://docs.microsoft.com/en-us/aspnet/core).
+This includes incoming gRPC requests using
+[Grpc.AspNetCore](https://www.nuget.org/packages/Grpc.AspNetCore).
 
 ## Installation
 
diff --git a/src/OpenTelemetry.Instrumentation.Grpc/CHANGELOG.md b/src/OpenTelemetry.Instrumentation.Grpc/CHANGELOG.md
deleted file mode 100644
index d8c321bcf8f..00000000000
--- a/src/OpenTelemetry.Instrumentation.Grpc/CHANGELOG.md
+++ /dev/null
@@ -1,20 +0,0 @@
-# Changelog
-
-## Unreleased
-
-* Grpc Instrumentation automatically populates HttpRequest in
-  Activity custom property
-  ([#1099](https://github.com/open-telemetry/opentelemetry-dotnet/pull/1099))
-  ([#1128](https://github.com/open-telemetry/opentelemetry-dotnet/pull/1128))
-
-## 0.4.0-beta.2
-
-Released 2020-07-24
-
-* First beta release
-
-## 0.3.0-beta
-
-Released 2020-07-23
-
-* Initial release
diff --git a/src/OpenTelemetry.Instrumentation.Grpc/README.md b/src/OpenTelemetry.Instrumentation.Grpc/README.md
deleted file mode 100644
index 9dc726a07db..00000000000
--- a/src/OpenTelemetry.Instrumentation.Grpc/README.md
+++ /dev/null
@@ -1,15 +0,0 @@
-# OpenTelemetry.Instrumentation.Grpc
-
-[![NuGet](https://img.shields.io/nuget/v/OpenTelemetry.Instrumentation.Grpc.svg)](https://www.nuget.org/packages/OpenTelemetry.Instrumentation.Grpc)
-[![NuGet](https://img.shields.io/nuget/dt/OpenTelemetry.Instrumentation.Grpc.svg)](https://www.nuget.org/packages/OpenTelemetry.Instrumentation.Grpc)
-
-## Installation
-
-```shell
-dotnet add package OpenTelemetry.Instrumentation.Grpc
-```
-
-## References
-
-* [gRPC for .NET](https://github.com/grpc/grpc-dotnet)
-* [OpenTelemetry Project](https://opentelemetry.io/)
diff --git a/src/OpenTelemetry.Instrumentation.Grpc/AssemblyInfo.cs b/src/OpenTelemetry.Instrumentation.GrpcNetClient/AssemblyInfo.cs
similarity index 100%
rename from src/OpenTelemetry.Instrumentation.Grpc/AssemblyInfo.cs
rename to src/OpenTelemetry.Instrumentation.GrpcNetClient/AssemblyInfo.cs
diff --git a/src/OpenTelemetry.Instrumentation.GrpcNetClient/CHANGELOG.md b/src/OpenTelemetry.Instrumentation.GrpcNetClient/CHANGELOG.md
new file mode 100644
index 00000000000..b0f0bfc99ad
--- /dev/null
+++ b/src/OpenTelemetry.Instrumentation.GrpcNetClient/CHANGELOG.md
@@ -0,0 +1,25 @@
+# Changelog
+
+## Unreleased
+
+* NuGet package renamed to OpenTelemetry.Instrumentation.GrpcNetClient to
+  more clearly indicate that this package is specifically for gRPC client
+  instrumentation. The package was previously named
+  OpenTelemetry.Instrumentation.Grpc.
+  ([#1136](https://github.com/open-telemetry/opentelemetry-dotnet/pull/1136))
+* Grpc.Net.Client Instrumentation automatically populates HttpRequest in
+  Activity custom property
+  ([#1099](https://github.com/open-telemetry/opentelemetry-dotnet/pull/1099))
+  ([#1128](https://github.com/open-telemetry/opentelemetry-dotnet/pull/1128))
+
+## 0.4.0-beta.2
+
+Released 2020-07-24
+
+* First beta release
+
+## 0.3.0-beta
+
+Released 2020-07-23
+
+* Initial release
diff --git a/src/OpenTelemetry.Instrumentation.Grpc/GrpcClientInstrumentation.cs b/src/OpenTelemetry.Instrumentation.GrpcNetClient/GrpcClientInstrumentation.cs
similarity index 93%
rename from src/OpenTelemetry.Instrumentation.Grpc/GrpcClientInstrumentation.cs
rename to src/OpenTelemetry.Instrumentation.GrpcNetClient/GrpcClientInstrumentation.cs
index 6c74aa6e44d..10b3f99f01e 100644
--- a/src/OpenTelemetry.Instrumentation.Grpc/GrpcClientInstrumentation.cs
+++ b/src/OpenTelemetry.Instrumentation.GrpcNetClient/GrpcClientInstrumentation.cs
@@ -14,10 +14,10 @@
 // limitations under the License.
 // </copyright>
 using System;
-using OpenTelemetry.Instrumentation.Grpc.Implementation;
+using OpenTelemetry.Instrumentation.GrpcNetClient.Implementation;
 using OpenTelemetry.Trace;
 
-namespace OpenTelemetry.Instrumentation.Grpc
+namespace OpenTelemetry.Instrumentation.GrpcNetClient
 {
     /// <summary>
     /// GrpcClient instrumentation.
diff --git a/src/OpenTelemetry.Instrumentation.Grpc/GrpcTagHelper.cs b/src/OpenTelemetry.Instrumentation.GrpcNetClient/GrpcTagHelper.cs
similarity index 97%
rename from src/OpenTelemetry.Instrumentation.Grpc/GrpcTagHelper.cs
rename to src/OpenTelemetry.Instrumentation.GrpcNetClient/GrpcTagHelper.cs
index 5f6767bcef0..cadd4199e45 100644
--- a/src/OpenTelemetry.Instrumentation.Grpc/GrpcTagHelper.cs
+++ b/src/OpenTelemetry.Instrumentation.GrpcNetClient/GrpcTagHelper.cs
@@ -18,7 +18,7 @@
 using System.Text.RegularExpressions;
 using OpenTelemetry.Trace;
 
-namespace OpenTelemetry.Instrumentation.Grpc
+namespace OpenTelemetry.Instrumentation.GrpcNetClient
 {
     internal static class GrpcTagHelper
     {
diff --git a/src/OpenTelemetry.Instrumentation.Grpc/Implementation/GrpcClientDiagnosticListener.cs b/src/OpenTelemetry.Instrumentation.GrpcNetClient/Implementation/GrpcClientDiagnosticListener.cs
similarity index 98%
rename from src/OpenTelemetry.Instrumentation.Grpc/Implementation/GrpcClientDiagnosticListener.cs
rename to src/OpenTelemetry.Instrumentation.GrpcNetClient/Implementation/GrpcClientDiagnosticListener.cs
index d286c3fd265..ad2907fe8f1 100644
--- a/src/OpenTelemetry.Instrumentation.Grpc/Implementation/GrpcClientDiagnosticListener.cs
+++ b/src/OpenTelemetry.Instrumentation.GrpcNetClient/Implementation/GrpcClientDiagnosticListener.cs
@@ -18,7 +18,7 @@
 using System.Net.Http;
 using OpenTelemetry.Trace;
 
-namespace OpenTelemetry.Instrumentation.Grpc.Implementation
+namespace OpenTelemetry.Instrumentation.GrpcNetClient.Implementation
 {
     internal class GrpcClientDiagnosticListener : ListenerHandler
     {
diff --git a/src/OpenTelemetry.Instrumentation.Grpc/Implementation/GrpcInstrumentationEventSource.cs b/src/OpenTelemetry.Instrumentation.GrpcNetClient/Implementation/GrpcInstrumentationEventSource.cs
similarity index 95%
rename from src/OpenTelemetry.Instrumentation.Grpc/Implementation/GrpcInstrumentationEventSource.cs
rename to src/OpenTelemetry.Instrumentation.GrpcNetClient/Implementation/GrpcInstrumentationEventSource.cs
index 5fe7fc8cde4..61d3b93337e 100644
--- a/src/OpenTelemetry.Instrumentation.Grpc/Implementation/GrpcInstrumentationEventSource.cs
+++ b/src/OpenTelemetry.Instrumentation.GrpcNetClient/Implementation/GrpcInstrumentationEventSource.cs
@@ -16,7 +16,7 @@
 
 using System.Diagnostics.Tracing;
 
-namespace OpenTelemetry.Instrumentation.Grpc.Implementation
+namespace OpenTelemetry.Instrumentation.GrpcNetClient.Implementation
 {
     /// <summary>
     /// EventSource events emitted from the project.
diff --git a/src/OpenTelemetry.Instrumentation.Grpc/Implementation/PropertyFetcher.cs b/src/OpenTelemetry.Instrumentation.GrpcNetClient/Implementation/PropertyFetcher.cs
similarity index 98%
rename from src/OpenTelemetry.Instrumentation.Grpc/Implementation/PropertyFetcher.cs
rename to src/OpenTelemetry.Instrumentation.GrpcNetClient/Implementation/PropertyFetcher.cs
index 635b1475b72..dab85e0874d 100644
--- a/src/OpenTelemetry.Instrumentation.Grpc/Implementation/PropertyFetcher.cs
+++ b/src/OpenTelemetry.Instrumentation.GrpcNetClient/Implementation/PropertyFetcher.cs
@@ -17,7 +17,7 @@
 using System.Linq;
 using System.Reflection;
 
-namespace OpenTelemetry.Instrumentation.Grpc.Implementation
+namespace OpenTelemetry.Instrumentation.GrpcNetClient.Implementation
 {
     internal class PropertyFetcher
     {
diff --git a/src/OpenTelemetry.Instrumentation.Grpc/OpenTelemetry.Instrumentation.Grpc.csproj b/src/OpenTelemetry.Instrumentation.GrpcNetClient/OpenTelemetry.Instrumentation.GrpcNetClient.csproj
similarity index 82%
rename from src/OpenTelemetry.Instrumentation.Grpc/OpenTelemetry.Instrumentation.Grpc.csproj
rename to src/OpenTelemetry.Instrumentation.GrpcNetClient/OpenTelemetry.Instrumentation.GrpcNetClient.csproj
index 1cabc94ae47..8a05774ef21 100644
--- a/src/OpenTelemetry.Instrumentation.Grpc/OpenTelemetry.Instrumentation.Grpc.csproj
+++ b/src/OpenTelemetry.Instrumentation.GrpcNetClient/OpenTelemetry.Instrumentation.GrpcNetClient.csproj
@@ -1,7 +1,7 @@
 <Project Sdk="Microsoft.NET.Sdk">
   <PropertyGroup>
     <TargetFrameworks>netstandard2.1</TargetFrameworks>
-    <Description>gRPC client instrumentation for OpenTelemetry .NET</Description>
+    <Description>gRPC for .NET client instrumentation for OpenTelemetry .NET</Description>
     <PackageTags>$(PackageTags);distributed-tracing</PackageTags>
   </PropertyGroup>
 
diff --git a/src/OpenTelemetry.Instrumentation.GrpcNetClient/README.md b/src/OpenTelemetry.Instrumentation.GrpcNetClient/README.md
new file mode 100644
index 00000000000..3684099eb4a
--- /dev/null
+++ b/src/OpenTelemetry.Instrumentation.GrpcNetClient/README.md
@@ -0,0 +1,18 @@
+# OpenTelemetry.Instrumentation.GrpcNetClient
+
+[![NuGet](https://img.shields.io/nuget/v/OpenTelemetry.Instrumentation.GrpcNetClient.svg)](https://www.nuget.org/packages/OpenTelemetry.Instrumentation.GrpcNetClient)
+[![NuGet](https://img.shields.io/nuget/dt/OpenTelemetry.Instrumentation.GrpcNetClient.svg)](https://www.nuget.org/packages/OpenTelemetry.Instrumentation.GrpcNetClient)
+
+Automatically instruments the outgoing requests from
+[Grpc.Net.Client](https://www.nuget.org/packages/Grpc.Net.Client).
+
+## Installation
+
+```shell
+dotnet add package OpenTelemetry.Instrumentation.GrpcNetClient
+```
+
+## References
+
+* [gRPC for .NET](https://github.com/grpc/grpc-dotnet)
+* [OpenTelemetry Project](https://opentelemetry.io/)
diff --git a/src/OpenTelemetry.Instrumentation.Grpc/TracerProviderBuilderExtensions.cs b/src/OpenTelemetry.Instrumentation.GrpcNetClient/TracerProviderBuilderExtensions.cs
similarity index 96%
rename from src/OpenTelemetry.Instrumentation.Grpc/TracerProviderBuilderExtensions.cs
rename to src/OpenTelemetry.Instrumentation.GrpcNetClient/TracerProviderBuilderExtensions.cs
index fa962b62d2c..bf595759879 100644
--- a/src/OpenTelemetry.Instrumentation.Grpc/TracerProviderBuilderExtensions.cs
+++ b/src/OpenTelemetry.Instrumentation.GrpcNetClient/TracerProviderBuilderExtensions.cs
@@ -15,7 +15,7 @@
 // </copyright>
 
 using System;
-using OpenTelemetry.Instrumentation.Grpc;
+using OpenTelemetry.Instrumentation.GrpcNetClient;
 
 namespace OpenTelemetry.Trace
 {
diff --git a/test/OpenTelemetry.Instrumentation.Grpc.Tests/EventSourceTest.cs b/test/OpenTelemetry.Instrumentation.Grpc.Tests/EventSourceTest.cs
index 9473a89602a..42dcec7782a 100644
--- a/test/OpenTelemetry.Instrumentation.Grpc.Tests/EventSourceTest.cs
+++ b/test/OpenTelemetry.Instrumentation.Grpc.Tests/EventSourceTest.cs
@@ -14,7 +14,7 @@
 // limitations under the License.
 // </copyright>
 
-using OpenTelemetry.Instrumentation.Grpc.Implementation;
+using OpenTelemetry.Instrumentation.GrpcNetClient.Implementation;
 using OpenTelemetry.Tests;
 using Xunit;
 
diff --git a/test/OpenTelemetry.Instrumentation.Grpc.Tests/GrpcTagHelperTests.cs b/test/OpenTelemetry.Instrumentation.Grpc.Tests/GrpcTagHelperTests.cs
index dd99d7ca779..d0dda40cae7 100644
--- a/test/OpenTelemetry.Instrumentation.Grpc.Tests/GrpcTagHelperTests.cs
+++ b/test/OpenTelemetry.Instrumentation.Grpc.Tests/GrpcTagHelperTests.cs
@@ -14,11 +14,11 @@
 // limitations under the License.
 // </copyright>
 using System.Diagnostics;
-using OpenTelemetry.Instrumentation.Grpc;
+using OpenTelemetry.Instrumentation.GrpcNetClient;
 using OpenTelemetry.Trace;
 using Xunit;
 
-namespace OpenTelemetry.Instrumentation.GrpcClient.Tests
+namespace OpenTelemetry.Instrumentation.Grpc.Tests
 {
     public class GrpcTagHelperTests
     {
diff --git a/test/OpenTelemetry.Instrumentation.Grpc.Tests/GrpcTests.client.cs b/test/OpenTelemetry.Instrumentation.Grpc.Tests/GrpcTests.client.cs
index 471c3c6f02f..ae0b7fcc775 100644
--- a/test/OpenTelemetry.Instrumentation.Grpc.Tests/GrpcTests.client.cs
+++ b/test/OpenTelemetry.Instrumentation.Grpc.Tests/GrpcTests.client.cs
@@ -20,8 +20,8 @@
 using Greet;
 using Grpc.Net.Client;
 using Moq;
-using OpenTelemetry.Instrumentation.Grpc.Implementation;
 using OpenTelemetry.Instrumentation.Grpc.Tests.Services;
+using OpenTelemetry.Instrumentation.GrpcNetClient.Implementation;
 using OpenTelemetry.Trace;
 using Xunit;
 
diff --git a/test/OpenTelemetry.Instrumentation.Grpc.Tests/OpenTelemetry.Instrumentation.Grpc.Tests.csproj b/test/OpenTelemetry.Instrumentation.Grpc.Tests/OpenTelemetry.Instrumentation.Grpc.Tests.csproj
index 9b4edef7969..aab3ea21eaa 100644
--- a/test/OpenTelemetry.Instrumentation.Grpc.Tests/OpenTelemetry.Instrumentation.Grpc.Tests.csproj
+++ b/test/OpenTelemetry.Instrumentation.Grpc.Tests/OpenTelemetry.Instrumentation.Grpc.Tests.csproj
@@ -1,6 +1,6 @@
 <Project Sdk="Microsoft.NET.Sdk">
   <PropertyGroup>
-    <Description>Unit test project for OpenTelemetry GrpcClient instrumentation</Description>
+    <Description>Unit test project for OpenTelemetry Grpc for .NET instrumentation</Description>
     <TargetFrameworks>netcoreapp3.1</TargetFrameworks>
   </PropertyGroup>
 
@@ -26,7 +26,7 @@
 
   <ItemGroup>
     <ProjectReference Include="$(RepoRoot)\src\OpenTelemetry.Instrumentation.AspNetCore\OpenTelemetry.Instrumentation.AspNetCore.csproj" />
-    <ProjectReference Include="$(RepoRoot)\src\OpenTelemetry.Instrumentation.Grpc\OpenTelemetry.Instrumentation.Grpc.csproj" />
+    <ProjectReference Include="$(RepoRoot)\src\OpenTelemetry.Instrumentation.GrpcNetClient\OpenTelemetry.Instrumentation.GrpcNetClient.csproj" />
     <ProjectReference Include="$(RepoRoot)\src\OpenTelemetry.Instrumentation.Http\OpenTelemetry.Instrumentation.Http.csproj" />
     <ProjectReference Include="$(RepoRoot)\src\OpenTelemetry\OpenTelemetry.csproj" />
     <Compile Include="$(RepoRoot)\test\OpenTelemetry.Tests\Shared\EventSourceTestHelper.cs" Link="EventSourceTestHelper.cs" />