diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index abd94779435..988509bdb06 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -79,6 +79,10 @@ New Features
 
 Bug fixes
 ~~~~~~~~~
+- Ensure an index of type ``CFTimeIndex`` is not converted to a ``DatetimeIndex`` when 
+  calling :py:meth:`Dataset.rename` (also :py:meth:`Dataset.rename_dims`
+  and :py:meth:`xr.Dataset.rename_vars`). By `Mathias Hauser <https://github.com/mathause>`_
+  (:issue:`3522`).
 - Fix a bug in `set_index` in case that an existing dimension becomes a level variable of MultiIndex. (:pull:`3520`)
   By `Keisuke Fujii <https://github.com/fujiisoup>`_.
 - Harmonize `_FillValue`, `missing_value` during encoding and decoding steps. (:pull:`3502`)
diff --git a/xarray/core/dataset.py b/xarray/core/dataset.py
index de713b830f2..793a55a87c2 100644
--- a/xarray/core/dataset.py
+++ b/xarray/core/dataset.py
@@ -2667,7 +2667,7 @@ def _rename_indexes(self, name_dict, dims_set):
                     verify_integrity=False,
                 )
             else:
-                index = pd.Index(v, name=new_name)
+                index = v.rename(new_name)
             indexes[new_name] = index
         return indexes
 
diff --git a/xarray/tests/test_dataset.py b/xarray/tests/test_dataset.py
index 67d3b3198dc..780843f2e61 100644
--- a/xarray/tests/test_dataset.py
+++ b/xarray/tests/test_dataset.py
@@ -8,6 +8,7 @@
 import numpy as np
 import pandas as pd
 import pytest
+from pandas.core.indexes.datetimes import DatetimeIndex
 
 import xarray as xr
 from xarray import (
@@ -22,6 +23,7 @@
     open_dataset,
     set_options,
 )
+from xarray.coding.cftimeindex import CFTimeIndex
 from xarray.core import dtypes, indexing, utils
 from xarray.core.common import duck_array_ops, full_like
 from xarray.core.npcompat import IS_NEP18_ACTIVE
@@ -2458,6 +2460,53 @@ def test_rename_vars(self):
         with pytest.raises(ValueError):
             original.rename_vars(names_dict_bad)
 
+    @requires_cftime
+    def test_rename_does_not_change_CFTimeIndex_type(self):
+        # make sure CFTimeIndex is not converted to DatetimeIndex #3522
+
+        time = xr.cftime_range(start="2000", periods=6, freq="2MS", calendar="noleap")
+        orig = Dataset(coords={"time": time})
+
+        renamed = orig.rename(time="time_new")
+        assert "time_new" in renamed.indexes
+        assert isinstance(renamed.indexes["time_new"], CFTimeIndex)
+        assert renamed.indexes["time_new"].name == "time_new"
+
+        # check original has not changed
+        assert "time" in orig.indexes
+        assert isinstance(orig.indexes["time"], CFTimeIndex)
+        assert orig.indexes["time"].name == "time"
+
+        # note: rename_dims(time="time_new") drops "ds.indexes"
+        renamed = orig.rename_dims()
+        assert isinstance(renamed.indexes["time"], CFTimeIndex)
+
+        renamed = orig.rename_vars()
+        assert isinstance(renamed.indexes["time"], CFTimeIndex)
+
+    def test_rename_does_not_change_DatetimeIndex_type(self):
+        # make sure DatetimeIndex is conderved on rename
+
+        time = pd.date_range(start="2000", periods=6, freq="2MS")
+        orig = Dataset(coords={"time": time})
+
+        renamed = orig.rename(time="time_new")
+        assert "time_new" in renamed.indexes
+        assert isinstance(renamed.indexes["time_new"], DatetimeIndex)
+        assert renamed.indexes["time_new"].name == "time_new"
+
+        # check original has not changed
+        assert "time" in orig.indexes
+        assert isinstance(orig.indexes["time"], DatetimeIndex)
+        assert orig.indexes["time"].name == "time"
+
+        # note: rename_dims(time="time_new") drops "ds.indexes"
+        renamed = orig.rename_dims()
+        assert isinstance(renamed.indexes["time"], DatetimeIndex)
+
+        renamed = orig.rename_vars()
+        assert isinstance(renamed.indexes["time"], DatetimeIndex)
+
     def test_swap_dims(self):
         original = Dataset({"x": [1, 2, 3], "y": ("x", list("abc")), "z": 42})
         expected = Dataset({"z": 42}, {"x": ("y", [1, 2, 3]), "y": list("abc")})