BUG: rename fails when using level

pandas/core/generic.py

@@ -1147,7 +1147,11 @@ def rename(
 
             # GH 13473
             if not callable(replacements):
-                indexer = ax.get_indexer_for(replacements)
+                if ax._is_multi and level is not None:
+                    indexer = ax.get_level_values(level).get_indexer_for(replacements)
+                else:
+                    indexer = ax.get_indexer_for(replacements)
+
                 if errors == "raise" and len(indexer[indexer == -1]):
                     missing_labels = [
                         label

pandas/tests/generic/test_series.py

@@ -151,3 +151,28 @@ def finalize(self, other, method=None, **kwargs):
         # reset
         Series._metadata = _metadata
         Series.__finalize__ = _finalize  # FIXME: use monkeypatch
+
+    # issue #43659
+    def test_rename_with_multiindex(self):
+        arrays = [
+            ["bar", "bar", "baz", "baz", "foo", "foo", "qux", "qux"],
+            ["one", "two", "one", "two", "one", "two", "one", "two"],
+        ]
+
+        tuples = list(zip(*arrays))
+        index = MultiIndex.from_tuples(tuples, names=["first", "second"])
+        s = Series(np.ones(8), index=index)
+        result = s.rename(index={"one": "yes"}, level="second", errors="raise")
+
+        arrays_expected = [
+            ["bar", "bar", "baz", "baz", "foo", "foo", "qux", "qux"],
+            ["yes", "two", "yes", "two", "yes", "two", "yes", "two"],
+        ]
+
+        tuples_expected = list(zip(*arrays_expected))
+        index_expected = MultiIndex.from_tuples(
+            tuples_expected, names=["first", "second"]
+        )
+        series_expected = Series(np.ones(8), index=index_expected)
+
+        assert result.equals(series_expected)