fix assign_coords multi-index: update coord names

Author: benbovy

xarray/core/coordinates.py

@@ -315,6 +315,7 @@ def _maybe_drop_multiindex_coords(self, coords: set[Hashable]) -> None:
         variables, indexes = drop_coords(
             coords, self._data._variables, self._data.xindexes
         )
+        self._data._coord_names.intersection_update(variables)
         self._data._variables = variables
         self._data._indexes = indexes
 

xarray/tests/test_dataset.py

@@ -4146,6 +4146,10 @@ def test_assign_coords_existing_multiindex(self) -> None:
         ):
             data.assign(x=range(4))
 
+        # https://github.com/pydata/xarray/issues/7097 (coord names updated)
+        updated = data.assign_coords(x=range(4))
+        assert len(updated.coords) == 1
+
     def test_assign_all_multiindex_coords(self) -> None:
         data = create_test_multiindex()
         actual = data.assign(x=range(4), level_1=range(4), level_2=range(4))