diff --git a/src/dual_model_variables.jl b/src/dual_model_variables.jl
index fe44042..384b667 100644
--- a/src/dual_model_variables.jl
+++ b/src/dual_model_variables.jl
@@ -80,6 +80,7 @@ function _add_dual_variable(
     # Add each vi to the dictionary
     func = MOI.get(primal_model, MOI.ConstraintFunction(), ci)
     set = MOI.get(primal_model, MOI.ConstraintSet(), ci)
+    is_unique_var = length(vis) == 1
     for (i, vi) in enumerate(vis)
         if !(F <: MOI.VectorOfVariables)
             value = set_dot(i, set, T) * _get_normalized_constant(func, set, i)
@@ -89,7 +90,8 @@ function _add_dual_variable(
         end
         if !is_empty(dual_names) && !isempty(ci_name)
             pre = dual_names.dual_variable_name_prefix
-            MOI.set(dual_model, MOI.VariableName(), vi, pre * ci_name * "_$i")
+            pos = is_unique_var ? "" : "_$i"
+            MOI.set(dual_model, MOI.VariableName(), vi, pre * ci_name * pos)
         end
     end
     return
diff --git a/test/Tests/test_JuMP_dualize.jl b/test/Tests/test_JuMP_dualize.jl
index 6d92b63..bb80506 100644
--- a/test/Tests/test_JuMP_dualize.jl
+++ b/test/Tests/test_JuMP_dualize.jl
@@ -64,7 +64,7 @@ end
 
         dual_model = dualize(model; dual_names = DualNames("dual", ""))
 
-        @test typeof(dual_model[:dualeqcon_1]) == VariableRef
+        @test typeof(dual_model[:dualeqcon]) == VariableRef
         @test !haskey(dual_model, Symbol(""))
     end
     @testset "JuMP_dualize_kwargs" begin
diff --git a/test/Tests/test_dual_names.jl b/test/Tests/test_dual_names.jl
index 9278846..87f9dc1 100644
--- a/test/Tests/test_dual_names.jl
+++ b/test/Tests/test_dual_names.jl
@@ -77,7 +77,7 @@
     }(
         1,
     )].dual_variables[1]
-    @test MOI.get(dual_model, MOI.VariableName(), vi_2) == "dualvar_lessthan_1"
+    @test MOI.get(dual_model, MOI.VariableName(), vi_2) == "dualvar_lessthan"
     # Query constraint names
     ci_1 =
         primal_dual_map.primal_variable_data[MOI.VariableIndex(