diff --git a/onnxscript/_internal/converter.py b/onnxscript/_internal/converter.py
index c2f6b0fb63..3789bb5f47 100644
--- a/onnxscript/_internal/converter.py
+++ b/onnxscript/_internal/converter.py
@@ -1108,7 +1108,12 @@ def ret(exp, i, suffix):
                 if val.value.is_graph_input():
                     # In ONNX, a graph-input cannot be an output of the graph.
                     # We need to insert a copy.
-                    return_var = self._emit_copy(return_var, preferred_name)
+                    copy_name = (
+                        exp.id
+                        if isinstance(exp, ast.Name) and exp.id != return_var.name
+                        else preferred_name
+                    )
+                    return_var = self._emit_copy(return_var, copy_name)
             for prev_output in self._current_fn.outputs:
                 if prev_output.name == return_var.name:
                     # ONNX does not allow duplicate output names.
diff --git a/onnxscript/_internal/converter_test.py b/onnxscript/_internal/converter_test.py
index c1fe276ef5..ea5eb1f339 100644
--- a/onnxscript/_internal/converter_test.py
+++ b/onnxscript/_internal/converter_test.py
@@ -607,6 +607,23 @@ def duplicate_output(X):
         outputs = duplicate_output.to_function_proto().output
         self.assertNotEqual(outputs[0], outputs[1])
 
+    def test_returned_input_alias_preserves_name(self):
+        @script(default_opset=op)
+        def returned_alias(X):
+            Y = X
+            return Y
+
+        function_proto = returned_alias.to_function_proto()
+        self.assertEqual(function_proto.output[0], "Y")
+        self.assertEqual(function_proto.node[-1].op_type, "Identity")
+        self.assertEqual(function_proto.node[-1].output[0], "Y")
+
+        @script(default_opset=op)
+        def returned_input(X):
+            return X
+
+        self.assertEqual(returned_input.to_function_proto().output[0], "return_val")
+
     def test_bool_attr_promotion(self):
         @script()
         def if_then_else(flag: bool, Y, Z):