What happened:
http://xarray.pydata.org/en/stable/generated/xarray.DataArray.rename.html#xarray.DataArray.rename
states that:

Returns a new DataArray with renamed coordinates or a new name.

What you expected to happen:
It should state:
"Returns a new DataArray with renamed coordinates, dimensions or a new name."
Since it definitely can do that.

Minimal example

xr.DataArray([1, 2, 3]).rename({"dim_0": "new"})

Further
While at it: Dataset.rename als does not mention explicitly that you can rename coordinates.