id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
1364911775,I_kwDOAMm_X85RWuaf,7005,Cannot re-index or align objects with conflicting indexes,1797906,open,0,,,2,2022-09-07T16:22:46Z,2022-09-09T16:04:05Z,,NONE,,,,"### What happened?

I'm looking to rename the values of indices of an existing dataset, for both regular and multi-index. i.e. you might start with a dataset with and index `[1,2,3]` and you want to rename those to `[""foo"", ""bar"", ""bar""]`.

I appear to be able to rename a couple using the method I've written, though renaming a second multi-index in the same `xr.Dataset` causes a `ValueError` I am struggling to interpret.

> cannot re-index or align objects with conflicting indexes found for the following dimensions: 'x' (2 conflicting indexes)
Conflicting indexes may occur when
> - they relate to different sets of coordinate and/or dimension names
> - they don't have the same type
> - they may be used to reindex data along common dimensions

### What did you expect to happen?

I start with the `xr.Datset`:

```
xarray.DataArray (x: 6, y: 6, z: 3)>
array(...)
Coordinates:
  * x            (x) object MultiIndex
  * x_one    (x) object 'a' 'a' 'b' 'b' 'c' 'c'
  * x_two    (x) int64 0 1 0 1 0 1
  * y            (y) object MultiIndex
  * y_one    (y) object 'a' 'a' 'b' 'b' 'c' 'c'
  * y_two    (y) int64 0 1 0 1 0 1
  * z            (z) int64 0 1 2
 ```

And remap the `z`, `x_one`, and `y_one` values to:

```
xarray.DataArray (x: 6, y: 6, z: 3)>
array(...)
Coordinates:
  * x            (x) object MultiIndex
  * x_one    (x) object 'aa' 'aa' 'bb' 'bb' 'cc' 'cc'
  * x_two    (x) int64 0 1 0 1 0 1
  * y            (y) object MultiIndex
  * y_one    (y) object 'aa' 'aa' 'bb' 'bb' 'cc' 'cc'
  * y_two    (y) int64 0 1 0 1 0 1
  * z            (z) <U4 'zero' 'one' 'two'
```

### Minimal Complete Verifiable Example

```Python
import numpy as np
import pandas as pd
import xarray as xr


def map_coords(ds, *, name, mapping):
    """"""
    Takes a xarray dataset's coordinate values and updates
    them with the given the provided mapping.

    Can handle both regular indices and multi-level indices.

    ds: the datasets
    name: name of the coordinate to update
    mapping: dictionary, key of old value, value of new value.
    """"""
    coord = ds.coords[name]
    old_values = coord.values.tolist()
    new_values = [mapping[v] for v in old_values]
    ds.coords[name] = xr.DataArray(new_values, coords=coord.coords)
    ds.coords[name].attrs = dict(coord.attrs)

midx = pd.MultiIndex.from_product([list(""abc""), [0, 1]], names=(""x_one"", ""x_two""))
midy = pd.MultiIndex.from_product([list(""abc""), [0, 1]], names=(""y_one"", ""y_two""))

mda = xr.DataArray(np.random.rand(6, 6, 3), [(""x"", midx), (""y"", midy), (""z"", range(3))])

map_coords(mda, name=""z"", mapping={0: ""zero"", 1: ""one"", 2: ""two""}). # success
map_coords(mda, name=""x_one"", mapping={""a"": ""aa"", ""b"": ""bb"", ""c"": ""cc""})  # success
map_coords(mda, name=""y_one"", mapping={""a"": ""aa"", ""b"": ""bb"", ""c"": ""cc""})  # ValueError
```


### MVCE confirmation

- [X] Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
- [X] Complete example — the example is self-contained, including all data and the text of any traceback.
- [X] Verifiable example — the example copy & pastes into an IPython prompt or [Binder notebook](https://mybinder.org/v2/gh/pydata/xarray/main?urlpath=lab/tree/doc/examples/blank_template.ipynb), returning the result.
- [X] New issue — a search of GitHub Issues suggests this is not a duplicate.

### Relevant log output

```Python
Traceback (most recent call last):
  File ""./main.py"", line 30, in <module>
    map_coords(mda, name=""y_one"", mapping={""a"": ""aa"", ""b"": ""bb"", ""c"": ""cc""})
  File ""./main.py"", line 20, in map_coords
    ds.coords[name] = xr.DataArray(new_values, coords=coord.coords)
  File ""./.venv/lib/python3.10/site-packages/xarray/core/coordinates.py"", line 32, in __setitem__
    self.update({key: value})
  File ""./.venv/lib/python3.10/site-packages/xarray/core/coordinates.py"", line 162, in update
    coords, indexes = merge_coords(
  File ""./.venv/lib/python3.10/site-packages/xarray/core/merge.py"", line 561, in merge_coords
    aligned = deep_align(
  File ""./.venv/lib/python3.10/site-packages/xarray/core/alignment.py"", line 827, in deep_align
    aligned = align(
  File ""./.venv/lib/python3.10/site-packages/xarray/core/alignment.py"", line 764, in align
    aligner.align()
  File ""./.venv/lib/python3.10/site-packages/xarray/core/alignment.py"", line 550, in align
    self.assert_no_index_conflict()
  File ""./.venv/lib/python3.10/site-packages/xarray/core/alignment.py"", line 319, in assert_no_index_conflict
    raise ValueError(
ValueError: cannot re-index or align objects with conflicting indexes found for the following dimensions: 'x' (2 conflicting indexes)
Conflicting indexes may occur when
- they relate to different sets of coordinate and/or dimension names
- they don't have the same type
- they may be used to reindex data along common dimensions
```


### Anything else we need to know?

I may also not be doing this remapping in the best way, this has been the easiest way I've found to do it. So maybe part of the problem is that, so open to alternative methods as well.

Thanks.

### Environment

<details>

INSTALLED VERSIONS
------------------
commit: None
python: 3.10.4 (main, Mar 28 2022, 15:33:01) [Clang 13.1.6 (clang-1316.0.21.2)]
python-bits: 64
OS: Darwin
OS-release: 21.6.0
machine: x86_64
processor: i386
byteorder: little
LC_ALL: None
LANG: en_GB.UTF-8
LOCALE: ('en_US', 'UTF-8')
libhdf5: 1.12.2
libnetcdf: None

xarray: 2022.6.0
pandas: 1.4.4
numpy: 1.23.2
scipy: 1.9.1
netCDF4: None
pydap: None
h5netcdf: 1.0.2
h5py: 3.7.0
Nio: None
zarr: None
cftime: None
nc_time_axis: None
PseudoNetCDF: None
rasterio: None
cfgrib: None
iris: None
bottleneck: None
dask: None
distributed: None
matplotlib: None
cartopy: None
seaborn: None
numbagg: None
fsspec: None
cupy: None
pint: None
sparse: None
flox: None
numpy_groupies: None
setuptools: 63.4.3
pip: 22.2.2
conda: None
pytest: None
IPython: None
sphinx: None
</details>
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