diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 351424fbb9f..5a9f2497ed6 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -65,6 +65,9 @@ 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>`_.
+- Raise an error when trying to use :py:meth:`Dataset.rename_dims` to
+  rename to an existing name (:issue:`3438`, :pull:`3645`)
+  By `Justus Magin <https://github.com/keewis>`_.
 - :py:meth:`Dataset.rename`, :py:meth:`DataArray.rename` now check for conflicts with
   MultiIndex level names.
 
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index 607350c8101..ac0a923db78 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -2798,7 +2798,8 @@ def rename_dims(
         ----------
         dims_dict : dict-like, optional
             Dictionary whose keys are current dimension names and
-            whose values are the desired names.
+            whose values are the desired names. The desired names must
+            not be the name of an existing dimension or Variable in the Dataset.
         **dims, optional
             Keyword form of ``dims_dict``.
             One of dims_dict or dims must be provided.
@@ -2816,12 +2817,17 @@ def rename_dims(
         DataArray.rename
         """
         dims_dict = either_dict_or_kwargs(dims_dict, dims, "rename_dims")
-        for k in dims_dict:
+        for k, v in dims_dict.items():
             if k not in self.dims:
                 raise ValueError(
                     "cannot rename %r because it is not a "
                     "dimension in this dataset" % k
                 )
+            if v in self.dims or v in self:
+                raise ValueError(
+                    f"Cannot rename {k} to {v} because {v} already exists. "
+                    "Try using swap_dims instead."
+                )
 
         variables, coord_names, sizes, indexes = self._rename_all(
             name_dict={}, dims_dict=dims_dict
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index 48d8c25b810..2220abbef31 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -2444,6 +2444,9 @@ def test_rename_dims(self):
         with pytest.raises(ValueError):
             original.rename_dims(dims_dict_bad)
 
+        with pytest.raises(ValueError):
+            original.rename_dims({"x": "z"})
+
     def test_rename_vars(self):
         original = Dataset({"x": ("x", [0, 1, 2]), "y": ("x", [10, 11, 12]), "z": 42})
         expected = Dataset(