diff --git a/xarray/core/coordinates.py b/xarray/core/coordinates.py
index 42cc8130810..47350b9403f 100644
--- a/xarray/core/coordinates.py
+++ b/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
 
@@ -441,7 +442,7 @@ def drop_coords(
                 f"other variables: {list(maybe_midx.index.names)!r}. "
                 f"This will raise an error in the future. Use `.drop_vars({idx_coord_names!r})` before "
                 "assigning new coordinate values.",
-                DeprecationWarning,
+                FutureWarning,
                 stacklevel=4,
             )
             for k in idx_coord_names:
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index 3602b87102d..bdbf2deac12 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -1501,9 +1501,7 @@ def test_assign_coords(self) -> None:
 
     def test_assign_coords_existing_multiindex(self) -> None:
         data = self.mda
-        with pytest.warns(
-            DeprecationWarning, match=r"Updating MultiIndexed coordinate"
-        ):
+        with pytest.warns(FutureWarning, match=r"Updating MultiIndexed coordinate"):
             data.assign_coords(x=range(4))
 
     def test_coords_alignment(self) -> None:
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index bc6410a6d4a..07ac491a10c 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -4136,16 +4136,16 @@ def test_assign_multiindex_level(self) -> None:
 
     def test_assign_coords_existing_multiindex(self) -> None:
         data = create_test_multiindex()
-        with pytest.warns(
-            DeprecationWarning, match=r"Updating MultiIndexed coordinate"
-        ):
+        with pytest.warns(FutureWarning, match=r"Updating MultiIndexed coordinate"):
             data.assign_coords(x=range(4))
 
-        with pytest.warns(
-            DeprecationWarning, match=r"Updating MultiIndexed coordinate"
-        ):
+        with pytest.warns(FutureWarning, match=r"Updating MultiIndexed coordinate"):
             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))