This has been discussed in #4825.

A third option for rename{_vars} would be to rename the coordinate and its index (if any), regardless of whether the old and new names correspond to existing dimensions. We plan to drop the concept of a "dimension coordinate" with an implicit index in favor of indexes explicitly part of Xarray's data model (see https://github.com/pydata/xarray/projects/1), so that it will be possible to set indexes for non-dimension coordinates and/or set dimension coordinates without indexes.

Re your example, in #5692 data.rename({"c": "x"}) does not implicitly create anymore an indexed coordinate (no *):

```python data_renamed

<xarray.DataArray (x: 3)>

array([5, 6, 7])

Coordinates:

x (x) int64 1 2 3

```

Instead, it should be possible to directly set an index for the c coordinate without the need to rename it, e.g.,

```python

API has still to be defined

data_indexed = data.set_index("c", index_cls=xr.PandasIndex)

data_indexed.sel(c=[1, 2])

<xarray.DataArray (x: 2)>

array([5, 6])

Coordinates:

* c (x) int64 1 2

```