diff --git a/pandas/core/series.py b/pandas/core/series.py
index f8875555fdf97..93e1579738a50 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -4726,6 +4726,13 @@ def rename(
                 errors=errors,
             )
         else:
+            # since _set_name supports only inplace and not copy param
+            # we determine inplace based on copy (if inplace is False)
+            # 1) If inplace is True, the value of copy is ignored
+            # 2) If inplace is False/not supplied(default case), then
+            #    inplace is determined based on copy (opposite of copy)
+            if not inplace:
+                inplace = not copy
             return self._set_name(index, inplace=inplace)
 
     @Appender(
diff --git a/pandas/tests/series/methods/test_rename.py b/pandas/tests/series/methods/test_rename.py
index 93c4fbb7f3c46..1179cd762cde8 100644
--- a/pandas/tests/series/methods/test_rename.py
+++ b/pandas/tests/series/methods/test_rename.py
@@ -174,3 +174,9 @@ def test_rename_copy_false(self, using_copy_on_write):
         else:
             assert ser[0] == shallow_copy[0]
             assert ser[1] == shallow_copy[9]
+
+    def test_rename_scalar_copy_false(self):
+        # GH 52450
+        ser = Series([1])
+        shallow_copy = ser.rename("series_a", copy=False)
+        assert id(ser) == id(shallow_copy)