MCVE Code Sample

```python

import xarray as xr da = xr.DataArray([0, 1], dims=["location"], coords={"lat": ("location", [10, 11]), "lon": ("location", [20, 21])}).set_index(location=["lat", "lon"]) da2 = xr.DataArray([2, 3], dims=["location"], coords={"lat": ("location", [12, 13]), "lon": ("location", [22, 23])}).set_index(location=["lat", "lon"]) xr.concat([da["location"], da2["location"]], dim="location") Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/harry/code/xarray/xarray/core/concat.py", line 135, in concat return f(objs, dim, data_vars, coords, compat, positions, fill_value, join) File "/home/harry/code/xarray/xarray/core/concat.py", line 431, in _dataarray_concat ds = _dataset_concat( File "/home/harry/code/xarray/xarray/core/concat.py", line 384, in _dataset_concat result = Dataset(result_vars, attrs=result_attrs) File "/home/harry/code/xarray/xarray/core/dataset.py", line 541, in init variables, coord_names, dims, indexes = merge_data_and_coords( File "/home/harry/code/xarray/xarray/core/merge.py", line 466, in merge_data_and_coords return merge_core( File "/home/harry/code/xarray/xarray/core/merge.py", line 556, in merge_core assert_unique_multiindex_level_names(variables) File "/home/harry/code/xarray/xarray/core/variable.py", line 2363, in assert_unique_multiindex_level_names raise ValueError("conflicting MultiIndex level name(s):\n%s" % conflict_str) ValueError: conflicting MultiIndex level name(s): 'lat' (location), 'lat' (<this-array>) 'lon' (location), 'lon' (<this-array>) ```

Expected Output

The output should be the same as first concatenating the DataArrays, then extracting the dimension location:

```python

xr.concat([da, da2], dim="location")["location"] <xarray.DataArray 'location' (location: 4)> array([(10, 20), (11, 21), (12, 22), (13, 23)], dtype=object) Coordinates: * location (location) MultiIndex - lat (location) int64 10 11 12 13 - lon (location) int64 20 21 22 23 ```

Problem Description

```python

da["location"] looks like a normal DataArray

location = da["location"] location <xarray.DataArray 'location' (location: 2)> array([(10, 20), (11, 21)], dtype=object) Coordinates: * location (location) MultiIndex - lat (location) int64 10 11 - lon (location) int64 20 21

but in actual fact, the variable._data is a MultiIndex

location.variable._data PandasIndexAdapter(array=MultiIndex([(10, 20), (11, 21)], names=['lat', 'lon']), dtype=dtype('O')) ```

This is why an error is thrown: variable.assert_unique_multiindex_level_names gets passed two variables: location.variable (the DataArray data values), and also location["location"].variable (the coordinate values), which are both MultiIndexes.

Output of xr.show_versions()