diff --git a/src/Bridges/Variable/bridges/ParameterToEqualToBridge.jl b/src/Bridges/Variable/bridges/ParameterToEqualToBridge.jl
index d740e61033..61f8205bce 100644
--- a/src/Bridges/Variable/bridges/ParameterToEqualToBridge.jl
+++ b/src/Bridges/Variable/bridges/ParameterToEqualToBridge.jl
@@ -58,3 +58,29 @@ function MOI.Bridges.inverse_adjoint_map_function(
 )
     return f
 end
+
+function MOI.supports(
+    ::MOI.ModelLike,
+    ::MOI.VariableName,
+    ::Type{<:ParameterToEqualToBridge},
+)
+    return true
+end
+
+function MOI.get(
+    model::MOI.ModelLike,
+    attr::MOI.VariableName,
+    bridge::ParameterToEqualToBridge,
+)
+    return MOI.get(model, attr, bridge.variable)
+end
+
+function MOI.set(
+    model::MOI.ModelLike,
+    attr::MOI.VariableName,
+    bridge::ParameterToEqualToBridge,
+    name::String,
+)
+    MOI.set(model, attr, bridge.variable, name)
+    return
+end
diff --git a/src/Bridges/bridge_optimizer.jl b/src/Bridges/bridge_optimizer.jl
index 02598ff409..5e59dc391c 100644
--- a/src/Bridges/bridge_optimizer.jl
+++ b/src/Bridges/bridge_optimizer.jl
@@ -1751,6 +1751,10 @@ function MOI.get(
     vi::MOI.VariableIndex,
 )
     if is_bridged(b, vi)
+        bridge_ = bridge(b, vi)
+        if MOI.supports(b, MOI.VariableName(), typeof(bridge_))
+            return MOI.get(b, MOI.VariableName(), bridge_)
+        end
         return get(b.var_to_name, vi, "")
     else
         return MOI.get(b.model, attr, vi)
@@ -1764,8 +1768,13 @@ function MOI.set(
     name::String,
 )
     if is_bridged(b, vi)
-        b.var_to_name[vi] = name
-        b.name_to_var = nothing # Invalidate the name map.
+        bridge_ = bridge(b, vi)
+        if MOI.supports(b, MOI.VariableName(), typeof(bridge_))
+            MOI.set(b, MOI.VariableName(), bridge_, name)
+        else
+            b.var_to_name[vi] = name
+            b.name_to_var = nothing # Invalidate the name map.
+        end
     else
         MOI.set(b.model, attr, vi, name)
     end
diff --git a/test/Bridges/bridge_optimizer.jl b/test/Bridges/bridge_optimizer.jl
index 4a4c1a3c04..3e23366a49 100644
--- a/test/Bridges/bridge_optimizer.jl
+++ b/test/Bridges/bridge_optimizer.jl
@@ -1570,6 +1570,28 @@ function test_issue_2817c()
     return
 end
 
+function test_issue_2762_success()
+    inner = MOI.Utilities.Model{Float64}()
+    model = MOI.Bridges.Variable.ParameterToEqualTo{Float64}(inner)
+    p, _ = MOI.add_constrained_variable(model, MOI.Parameter(1.0))
+    MOI.set(model, MOI.VariableName(), p, "p")
+    @test MOI.get(model, MOI.VariableName(), p) == "p"
+    x = only(MOI.get(inner, MOI.ListOfVariableIndices()))
+    @test MOI.get(inner, MOI.VariableName(), x) == "p"
+    return
+end
+
+function test_issue_2762_fail()
+    inner = MOI.Utilities.Model{Float64}()
+    model = MOI.Bridges.Variable.NonposToNonneg{Float64}(inner)
+    y, _ = MOI.add_constrained_variables(model, MOI.Nonpositives(2))
+    MOI.set(model, MOI.VariableName(), y[1], "y1")
+    @test MOI.get(model, MOI.VariableName(), y[1]) == "y1"
+    x = MOI.get(inner, MOI.ListOfVariableIndices())
+    @test all(isempty, MOI.get(inner, MOI.VariableName(), x))
+    return
+end
+
 end  # module
 
 TestBridgeOptimizer.runtests()