add multiindex level name checking to .rename()

doc/whats-new.rst

@@ -62,6 +62,8 @@ Bug fixes
   By `Tom Augspurger <https://github.com/TomAugspurger>`_.
 - Ensure :py:meth:`Dataset.quantile`, :py:meth:`DataArray.quantile` issue the correct error
   when ``q`` is out of bounds (:issue:`3634`) by `Mathias Hauser <https://github.com/mathause>`_.
+- :py:meth:`Dataset.rename`, :py:meth:`DataArray.rename` now check for conflicts with
+  MultiIndex level names.
 
 Documentation
 ~~~~~~~~~~~~~

xarray/core/dataset.py

@@ -89,7 +89,13 @@
     is_scalar,
     maybe_wrap_array,
 )
-from .variable import IndexVariable, Variable, as_variable, broadcast_variables
+from .variable import (
+    IndexVariable,
+    Variable,
+    as_variable,
+    broadcast_variables,
+    assert_unique_multiindex_level_names,
+)
 
 if TYPE_CHECKING:
     from ..backends import AbstractDataStore, ZarrStore
@@ -2780,6 +2786,7 @@ def rename(
         variables, coord_names, dims, indexes = self._rename_all(
             name_dict=name_dict, dims_dict=name_dict
         )
+        assert_unique_multiindex_level_names(variables)
         return self._replace(variables, coord_names, dims=dims, indexes=indexes)
 
     def rename_dims(

xarray/tests/test_dataset.py

@@ -2461,6 +2461,14 @@ def test_rename_vars(self):
         with pytest.raises(ValueError):
             original.rename_vars(names_dict_bad)
 
+    def test_rename_multiindex(self):
+        mindex = pd.MultiIndex.from_tuples(
+            [([1, 2]), ([3, 4])], names=["level0", "level1"]
+        )
+        data = Dataset({}, {"x": mindex})
+        with raises_regex(ValueError, "conflicting MultiIndex"):
+            data.rename({"x": "level0"})
+
     @requires_cftime
     def test_rename_does_not_change_CFTimeIndex_type(self):
         # make sure CFTimeIndex is not converted to DatetimeIndex #3522