diff --git a/ext/DualizationJuMPExt/DualizationJuMPExt.jl b/ext/DualizationJuMPExt/DualizationJuMPExt.jl
index b59ec67..a42ce06 100644
--- a/ext/DualizationJuMPExt/DualizationJuMPExt.jl
+++ b/ext/DualizationJuMPExt/DualizationJuMPExt.jl
@@ -146,4 +146,14 @@ function Dualization._get_dual_parameter(
     return JuMP.VariableRef(dual_model, moi_dual_vi)
 end
 
+function Dualization._get_dual_slack_variable(
+    dual_model::JuMP.Model,
+    primal_ref::JuMP.VariableRef,
+)
+    map = _get_primal_dual_map(dual_model)
+    moi_primal_vi = JuMP.index(primal_ref)
+    moi_dual_vi = Dualization._get_dual_slack_variable(map, moi_primal_vi)
+    return JuMP.VariableRef(dual_model, moi_dual_vi)
+end
+
 end # module DualizationJuMPExt
diff --git a/src/dual_model_variables.jl b/src/dual_model_variables.jl
index 53358b6..980fb65 100644
--- a/src/dual_model_variables.jl
+++ b/src/dual_model_variables.jl
@@ -142,7 +142,7 @@ function _add_primal_parameter_vars(
             prefix =
                 dual_names.parameter_name_prefix == "" ? "param_" :
                 dual_names.parameter_name_prefix
-            MOI.set(dual_model, MOI.VariableName(), vi, prefix * vi_name)
+            MOI.set(dual_model, MOI.VariableName(), vis[i], prefix * vi_name)
         end
     end
     return
diff --git a/src/structures.jl b/src/structures.jl
index 6fc5914..3063a81 100644
--- a/src/structures.jl
+++ b/src/structures.jl
@@ -184,6 +184,10 @@ function _get_dual_parameter(m::PrimalDualMap, vi::MOI.VariableIndex)
     return m.primal_parameter_to_dual_parameter[vi]
 end
 
+function _get_dual_slack_variable(m::PrimalDualMap, vi::MOI.VariableIndex)
+    return m.primal_var_in_quad_obj_to_dual_slack_var[vi]
+end
+
 function Base.getproperty(m::PrimalDualMap{T}, name::Symbol) where {T}
     if name === :constrained_var_idx
         error(
diff --git a/test/Tests/test_JuMP_dualize.jl b/test/Tests/test_JuMP_dualize.jl
index 47c1c9a..5118256 100644
--- a/test/Tests/test_JuMP_dualize.jl
+++ b/test/Tests/test_JuMP_dualize.jl
@@ -128,4 +128,21 @@ end
         con = Dualization._get_dual_constraint(dual_model, cv)
         @test con isa ConstraintRef
     end
+    @testset "JuMP parametric quadratic" begin
+        model = Model()
+        @variable(model, x)
+        @variable(model, p ∈ Parameter(2.0))
+        @constraint(model, c, x <= p)
+        @objective(model, Max, 3x + x^2)
+        dual_model = dualize(model, dual_names = DualNames())
+        param = Dualization._get_dual_parameter(dual_model, p)
+        @test param isa VariableRef
+        @test owner_model(param) === dual_model
+        @test MOI.get(dual_model, MOI.VariableName(), param) == "param_p"
+        quadslack = Dualization._get_dual_slack_variable(dual_model, x)
+        @test quadslack isa VariableRef
+        @test owner_model(quadslack) === dual_model
+        @test MOI.get(dual_model, MOI.VariableName(), quadslack) ==
+              "quadslack_x"
+    end
 end
diff --git a/test/Tests/test_partial_dual_linear.jl b/test/Tests/test_partial_dual_linear.jl
index 9a3a5db..3cd4c71 100644
--- a/test/Tests/test_partial_dual_linear.jl
+++ b/test/Tests/test_partial_dual_linear.jl
@@ -99,6 +99,44 @@
         )
     end
 
+    @testset "lp1_test - parameter name" begin
+        #=
+        primal
+            min -4x_2 - 1
+        s.t.
+            x_1 >= 3         :y_2
+            x_1 + 2x_2 <= 3  :y_3
+        ignore x_2 during dualization
+        dual
+
+        s.t.
+            y_2 >= 0
+            y_3 <= 0
+            y_2 + y_3 == 0    :x_1
+        =#
+        primal_model = lp1_test()
+        MOI.add_constraint(
+            primal_model,
+            MOI.VariableIndex(2),
+            MOI.Parameter{Float64}(0.0),
+        )
+        dual = Dualization.dualize(
+            primal_model,
+            dual_names = Dualization.DualNames("", "", "parameter_", ""),
+        )
+        dual_model = dual.dual_model
+        primal_dual_map = dual.primal_dual_map
+        primal_parameter_to_dual_parameter =
+            primal_dual_map.primal_parameter_to_dual_parameter
+        @test MOI.get(
+            dual_model,
+            MOI.VariableName(),
+            primal_parameter_to_dual_parameter[MOI.VariableIndex(2)],
+        ) ==
+              "parameter_" *
+              MOI.get(primal_model, MOI.VariableName(), MOI.VariableIndex(2))
+    end
+
     @testset "lp7_test - x_1 ignored" begin
         #=
         primal