What happened?

We used Data{set,Array}.rename{_vars}({coord: dim_coord}) to make a coordinate a dimension coordinate (instead of set_index). This results in the coordinate correctly being displayed as a dimension coordinate (with the *) but it does not create an index, such that further operations like sel fail with a strange KeyError.

What did you expect to happen?

I expect one of two things to be true:

1. rename{_vars} does not allow setting dimension coordinates (raises Error and tells you to use set_index)
2. rename{_vars} checks for this occasion and sets the index correctly

Minimal Complete Verifiable Example

```python import xarray as xr

data = xr.DataArray([5, 6, 7], coords={"c": ("x", [1, 2, 3])}, dims="x")

<xarray.DataArray (x: 3)>

array([5, 6, 7])

Coordinates:

c (x) int64 1 2 3

Dimensions without coordinates: x

data_renamed = data.rename({"c": "x"})

<xarray.DataArray (x: 3)>

array([5, 6, 7])

Coordinates:

* x (x) int64 1 2 3

data_renamed.indexes

Empty

data_renamed.sel(x=2)

KeyError: 'no index found for coordinate x'

if we use set_index it works

data_indexed = data.set_index({"x": "c"})

looks the same as data_renamed!

<xarray.DataArray (x: 3)>

array([1, 2, 3])

Coordinates:

* x (x) int64 1 2 3

data_indexed.indexes

x: Int64Index([1, 2, 3], dtype='int64', name='x')

```

Relevant log output

No response

Anything else we need to know?

No response

Environment

INSTALLED VERSIONS

commit: None python: 3.9.1 (default, Jan 13 2021, 15:21:08) [GCC 4.8.5 20150623 (Red Hat 4.8.5-44)] python-bits: 64 OS: Linux OS-release: 3.10.0-1160.49.1.el7.x86_64 machine: x86_64 processor: x86_64 byteorder: little LC_ALL: None LANG: en_US.UTF-8 LOCALE: ('en_US', 'UTF-8') libhdf5: 1.12.0 libnetcdf: 4.7.4

xarray: 0.20.2 pandas: 1.3.5 numpy: 1.21.5 scipy: 1.7.3 netCDF4: 1.5.8 pydap: None h5netcdf: None h5py: None Nio: None zarr: None cftime: 1.5.1.1 nc_time_axis: None PseudoNetCDF: None rasterio: None cfgrib: None iris: None bottleneck: None dask: None distributed: None matplotlib: 3.5.1 cartopy: None seaborn: None numbagg: None fsspec: None cupy: None pint: None sparse: None setuptools: 49.2.1 pip: 22.0.2 conda: None pytest: 6.2.5 IPython: 8.0.0 sphinx: None