diff --git a/docs/src/submodules/Utilities/reference.md b/docs/src/submodules/Utilities/reference.md
index fcd88befeb..25054cc243 100644
--- a/docs/src/submodules/Utilities/reference.md
+++ b/docs/src/submodules/Utilities/reference.md
@@ -64,7 +64,6 @@ Utilities.latex_formulation
 ## Copy utilities
 
 ```@docs
-Utilities.automatic_copy_to
 Utilities.default_copy_to
 Utilities.IndexMap
 Utilities.identity_index_map
diff --git a/docs/src/tutorials/implementing.md b/docs/src/tutorials/implementing.md
index 432a12be0e..2560d4dddc 100644
--- a/docs/src/tutorials/implementing.md
+++ b/docs/src/tutorials/implementing.md
@@ -470,7 +470,7 @@ MOI.supports_incremental_interface(::Optimizer, copy_names::Bool) = true
 MOI.supports_incremental_interface(::Optimizer, copy_names::Bool) = !copy_names
 
 function MOI.copy_to(dest::Optimizer, src::MOI.ModelLike; kwargs...)
-    return MOI.Utilities.automatic_copy_to(dest, src; kwargs...)
+    return MOI.Utilities.default_copy_to(dest, src; kwargs...)
 end
 ```
 See [`supports_incremental_interface`](@ref) for more details on whether to
diff --git a/src/Bridges/bridge_optimizer.jl b/src/Bridges/bridge_optimizer.jl
index 7da990a94b..7e814d0a38 100644
--- a/src/Bridges/bridge_optimizer.jl
+++ b/src/Bridges/bridge_optimizer.jl
@@ -426,8 +426,12 @@ function MOIU.pass_nonvariable_constraints(
     return
 end
 
-function MOI.copy_to(b::AbstractBridgeOptimizer, src::MOI.ModelLike; kwargs...)
-    return MOIU.automatic_copy_to(b, src; kwargs...)
+function MOI.copy_to(
+    dest::AbstractBridgeOptimizer,
+    src::MOI.ModelLike;
+    kwargs...,
+)
+    return MOIU.default_copy_to(dest, src; kwargs...)
 end
 
 function MOI.supports_incremental_interface(
diff --git a/src/Utilities/copy.jl b/src/Utilities/copy.jl
index 09c0262441..27cdb7cb9f 100644
--- a/src/Utilities/copy.jl
+++ b/src/Utilities/copy.jl
@@ -1,39 +1,7 @@
 # This file contains default implementations for the `MOI.copy_to` function that
 # can be used by a model.
 
-"""
-    automatic_copy_to(
-        dest::MOI.ModelLike,
-        src::MOI.ModelLike;
-        copy_names::Bool=true,
-        filter_constraints::Union{Nothing,Function} = nothing,
-    )
-
-A default fallback for [`MOI.copy_to`](@ref).
-
-To use this method, define
-[`MathOptInterface.supports_incremental_interface`](@ref).
-
-If the `filter_constraints` arguments is given, only the constraints for which
-this function returns `true` will be copied. This function is given a
-constraint index as argument.
-"""
-function automatic_copy_to(
-    dest::MOI.ModelLike,
-    src::MOI.ModelLike;
-    copy_names::Bool = true,
-    filter_constraints::Union{Nothing,Function} = nothing,
-)
-    if !MOI.supports_incremental_interface(dest, copy_names)
-        error(
-            "Model $(typeof(dest)) does not support copy",
-            copy_names ? " with names" : "",
-            ".",
-        )
-    end
-    return default_copy_to(dest, src, copy_names, filter_constraints)
-end
-
+@deprecate automatic_copy_to default_copy_to
 @deprecate supports_default_copy_to MOI.supports_incremental_interface
 
 include("copy/index_map.jl")
@@ -486,14 +454,6 @@ function copy_free_variables(
     return
 end
 
-function default_copy_to(dest::MOI.ModelLike, src::MOI.ModelLike)
-    Base.depwarn(
-        "default_copy_to(dest, src) is deprecated, use default_copy_to(dest, src, true) instead or default_copy_to(dest, src, false) if you do not want to copy names.",
-        :default_copy_to,
-    )
-    return default_copy_to(dest, src, true)
-end
-
 function sorted_variable_sets_by_cost(dest::MOI.ModelLike, src::MOI.ModelLike)
     constraint_types = MOI.get(src, MOI.ListOfConstraintTypesPresent())
     single_or_vector_variables_types = [
@@ -575,29 +535,54 @@ only once all the model information is gathered.
 """
 function final_touch(::MOI.ModelLike, idxmap) end
 
+function default_copy_to(
+    dest::MOI.ModelLike,
+    src::MOI.ModelLike,
+    copy_names::Bool,
+    filter_constraints::Union{Nothing,Function} = nothing,
+)
+    @warn(
+        "The `copy_names` and `filter_constraints` arguments to " *
+        "`default_copy_to` are now keyword arguments.",
+        maxlog = 1,
+    )
+    return default_copy_to(
+        dest,
+        src;
+        copy_names = copy_names,
+        filter_constraints = filter_constraints,
+    )
+end
+
 """
     default_copy_to(
         dest::MOI.ModelLike,
-        src::MOI.ModelLike,
-        copy_names::Bool,
+        src::MOI.ModelLike;
+        copy_names::Bool = true,
         filter_constraints::Union{Nothing,Function} = nothing,
     )
 
-Implements `MOI.copy_to(dest, src)` by adding the variables and then the
-constraints and attributes incrementally. The function
-[`MathOptInterface.supports_incremental_interface`](@ref) can be used to check
-whether `dest` supports the copying a model incrementally.
+A default implementation of `MOI.copy_to(dest, src)` for models that implement
+the incremental interface, i.e., [`MOI.supports_incremental_interface`](@ref)
+returns `true`.
 
-If the `filter_constraints` arguments is given, only the constraints for which
-this function returns `true` will be copied. This function is given a
-constraint index as argument.
+If `filter_constraints` is a `Function`, only constraints for which
+`filter_constraints(ci)` returns `true` will be copied, where `ci` is the
+[`MOI.ConstraintIndex`](@ref) of the constraint.
 """
 function default_copy_to(
     dest::MOI.ModelLike,
-    src::MOI.ModelLike,
-    copy_names::Bool,
+    src::MOI.ModelLike;
+    copy_names::Bool = true,
     filter_constraints::Union{Nothing,Function} = nothing,
 )
+    if !MOI.supports_incremental_interface(dest, copy_names)
+        error(
+            "Model $(typeof(dest)) does not support copy",
+            copy_names ? " with names" : "",
+            ".",
+        )
+    end
     MOI.empty!(dest)
 
     vis_src = MOI.get(src, MOI.ListOfVariableIndices())
diff --git a/src/Utilities/mockoptimizer.jl b/src/Utilities/mockoptimizer.jl
index a661af2507..b0fb34a730 100644
--- a/src/Utilities/mockoptimizer.jl
+++ b/src/Utilities/mockoptimizer.jl
@@ -11,8 +11,8 @@ struct MockConstraintAttribute <: MOI.AbstractConstraintAttribute end
 """
     MockOptimizer
 
-`MockOptimizer` is a fake optimizer especially useful for testing. Its main 
-feature is that it can store the values that should be returned for each 
+`MockOptimizer` is a fake optimizer especially useful for testing. Its main
+feature is that it can store the values that should be returned for each
 attribute.
 """
 mutable struct MockOptimizer{MT<:MOI.ModelLike} <: MOI.AbstractOptimizer
@@ -920,8 +920,8 @@ function MOI.supports_add_constrained_variables(
     return MOI.supports_add_constrained_variables(mock.inner_model, MOI.Reals)
 end
 
-function MOI.copy_to(mock::MockOptimizer, src::MOI.ModelLike; kws...)
-    return automatic_copy_to(mock, src; kws...)
+function MOI.copy_to(dest::MockOptimizer, src::MOI.ModelLike; kwargs...)
+    return default_copy_to(dest, src; kwargs...)
 end
 
 function MOI.supports_incremental_interface(
diff --git a/src/Utilities/model.jl b/src/Utilities/model.jl
index 56a136cc73..a9ef5d47ec 100644
--- a/src/Utilities/model.jl
+++ b/src/Utilities/model.jl
@@ -575,9 +575,10 @@ function pass_nonvariable_constraints(
     )
 end
 
-function MOI.copy_to(dest::AbstractModel, src::MOI.ModelLike; kws...)
-    return automatic_copy_to(dest, src; kws...)
+function MOI.copy_to(dest::AbstractModel, src::MOI.ModelLike; kwargs...)
+    return default_copy_to(dest, src; kwargs...)
 end
+
 MOI.supports_incremental_interface(::AbstractModel, ::Bool) = true
 function final_touch(model::AbstractModel, index_map)
     return final_touch(model.constraints, index_map)
diff --git a/src/Utilities/universalfallback.jl b/src/Utilities/universalfallback.jl
index bf55f26307..073b4f9d7f 100644
--- a/src/Utilities/universalfallback.jl
+++ b/src/Utilities/universalfallback.jl
@@ -128,8 +128,8 @@ function pass_nonvariable_constraints(
     )
 end
 
-function MOI.copy_to(uf::UniversalFallback, src::MOI.ModelLike; kws...)
-    return MOIU.automatic_copy_to(uf, src; kws...)
+function MOI.copy_to(dest::UniversalFallback, src::MOI.ModelLike; kwargs...)
+    return MOIU.default_copy_to(dest, src; kwargs...)
 end
 
 function MOI.supports_incremental_interface(
diff --git a/test/DeprecatedTest/modellike.jl b/test/DeprecatedTest/modellike.jl
index caafc10f3e..efae198a32 100644
--- a/test/DeprecatedTest/modellike.jl
+++ b/test/DeprecatedTest/modellike.jl
@@ -2,7 +2,7 @@ using Test
 import MathOptInterface
 const MOI = MathOptInterface
 const MOIT = MOI.DeprecatedTest
-const MOU = MOI.Utilities
+const MOIU = MOI.Utilities
 
 @testset "Start value attributes and nothing" begin
     model = MOIU.MockOptimizer(MOIU.UniversalFallback(MOIU.Model{Float64}()))
diff --git a/test/Utilities/cachingoptimizer.jl b/test/Utilities/cachingoptimizer.jl
index 4b70ac4905..1c49c78dde 100644
--- a/test/Utilities/cachingoptimizer.jl
+++ b/test/Utilities/cachingoptimizer.jl
@@ -85,7 +85,7 @@ end
 MOI.supports_incremental_interface(::NoFreeVariables, names::Bool) = !names
 
 function MOI.copy_to(dest::NoFreeVariables, src::MOI.ModelLike; kwargs...)
-    return MOI.Utilities.automatic_copy_to(dest, src; kwargs...)
+    return MOI.Utilities.default_copy_to(dest, src; kwargs...)
 end
 
 ###
diff --git a/test/Utilities/copy.jl b/test/Utilities/copy.jl
index fd4bd8145f..e63d1bd71c 100644
--- a/test/Utilities/copy.jl
+++ b/test/Utilities/copy.jl
@@ -30,9 +30,9 @@ function MOI.empty!(::AbstractDummyModel) end
 function MOI.copy_to(
     dest::AbstractDummyModel,
     src::MOI.ModelLike;
-    copy_names = true,
+    copy_names::Bool = true,
 )
-    return MOIU.default_copy_to(dest, src, copy_names)
+    return MOIU.default_copy_to(dest, src; copy_names = copy_names)
 end
 
 MOI.supports(::AbstractDummyModel, ::MOI.ObjectiveSense) = true
@@ -124,12 +124,12 @@ end
 function test_AUTOMATIC()
     src = DummyModel()
     dest = DummyModel()
-    @test_throws ErrorException MOIU.automatic_copy_to(dest, src)
+    @test_throws ErrorException MOIU.default_copy_to(dest, src)
     try
-        @test_throws ErrorException MOIU.automatic_copy_to(dest, src)
+        @test_throws ErrorException MOIU.default_copy_to(dest, src)
     catch err
         @test sprint(showerror, err) ==
-              "Model DummyModel does not" * " support copy with names."
+              "Model DummyModel does not support copy with names."
     end
 end
 
@@ -151,7 +151,7 @@ function test_issue_849()
     )
     MOI.set(model, MOI.NLPBlock(), nlp_data)
     copy = MOIU.UniversalFallback(MOIU.Model{Float64}())
-    index_map = MOIU.default_copy_to(copy, model, true)
+    index_map = MOIU.default_copy_to(copy, model; copy_names = true)
     for vi in [a, b, c, x, y[1]]
         @test index_map[vi] == vi
     end
@@ -186,9 +186,9 @@ end
 function MOI.copy_to(
     dest::ConstrainedVariablesModel,
     src::MOI.ModelLike;
-    kws...,
+    kwargs...,
 )
-    return MOIU.automatic_copy_to(dest, src; kws...)
+    return MOIU.default_copy_to(dest, src; kwargs...)
 end
 
 function MOI.add_variables(model::ConstrainedVariablesModel, n)
@@ -283,7 +283,7 @@ function MOI.copy_to(
     src::MOI.ModelLike;
     kwargs...,
 )
-    return MOIU.automatic_copy_to(dest, src; kwargs...)
+    return MOIU.default_copy_to(dest, src; kwargs...)
 end
 
 function MOI.supports_incremental_interface(
@@ -669,8 +669,8 @@ end
 
 MOI.supports_incremental_interface(::BoundModel, ::Bool) = true
 
-function MOI.copy_to(dest::BoundModel, src::MOI.ModelLike; kws...)
-    return MOIU.automatic_copy_to(dest, src; kws...)
+function MOI.copy_to(dest::BoundModel, src::MOI.ModelLike; kwargs...)
+    return MOIU.default_copy_to(dest, src; kwargs...)
 end
 
 MOI.empty!(model::BoundModel) = MOI.empty!(model.inner)
diff --git a/test/deprecate.jl b/test/deprecate.jl
index 803660c1b1..47d2b9877f 100644
--- a/test/deprecate.jl
+++ b/test/deprecate.jl
@@ -70,6 +70,13 @@ function test_RawOptimizerAttribute()
     @test_logs (:warn,) MOI.RawParameter(:a) == MOI.RawOptimizerAttribute("a")
 end
 
+function test_default_copy_to()
+    dest = MOI.Utilities.Model{Float64}()
+    src = MOI.Utilities.Model{Float64}()
+    @test_logs (:warn,) MOI.Utilities.default_copy_to(dest, src, true)
+    return
+end
+
 function runtests()
     for name in names(@__MODULE__; all = true)
         if startswith("$name", "test_")
diff --git a/test/dummy.jl b/test/dummy.jl
index 7a5bc8ff04..b6a8fa18c6 100644
--- a/test/dummy.jl
+++ b/test/dummy.jl
@@ -5,14 +5,19 @@ const MOIU = MOI.Utilities
 abstract type AbstractDummyModel <: MOI.ModelLike end
 
 function MOI.empty!(::AbstractDummyModel) end
+
 function MOI.copy_to(
     dest::AbstractDummyModel,
     src::MOI.ModelLike;
-    copy_names = true,
+    copy_names::Bool = true,
 )
     return MOIU.default_copy_to(dest, src, copy_names)
 end
+
+MOI.supports_incremental_interface(::AbstractDummyModel, ::Bool) = true
+
 MOI.supports(::AbstractDummyModel, ::MOI.ObjectiveSense) = true
+
 function MOI.supports(
     ::AbstractDummyModel,
     ::MOI.ConstraintPrimalStart,