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Description
Pandas version checks
- 
I have checked that this issue has not already been reported. 
- 
I have confirmed this bug exists on the latest version of pandas. 
- 
I have confirmed this bug exists on the main branch of pandas. 
Reproducible Example
import numpy as np
import pandas as pd
from natsort import index_natsorted
df = pd.DataFrame(
    [[1, 2], [3, 4]],
    columns=pd.MultiIndex.from_product([["a"], ["top10", "top2"]], names=("A", "B")),
)
df.sort_index(axis=1, level=1)  # Passes
df.sort_index(axis=1, level="B")  # Passes
df.sort_index(axis=1, level=1, key=lambda x: np.argsort(index_natsorted(x)))  # Passes
df.sort_index(axis=1, level="B", key=lambda x: np.argsort(index_natsorted(x)))  # Fails with KeyError: 'Level B not found'Issue Description
When sorting over a multi-index with level name and key being set, an error is raised.
Early investigations:
- in the sort process the name of the level is dropped, due to key
- Happens in ensure_key_mappedhttps://github.com/pandas-dev/pandas/blob/e209a35403f8835bbcff97636b83d2fc39b51e68/pandas/core/sorting.py#L547-592. Key is applied on the values of the index, which drops the name.
 
- Happens in 
- when sort_levelis called fromget_indexer_indexer, the sort is attempted on the level name, which has been dropped already
Expected Behavior
sort_index should support both level id or level name
Installed Versions
INSTALLED VERSIONS
commit                : c888af6
python                : 3.12.10
python-bits           : 64
OS                    : Windows
OS-release            : 11
Version               : 10.0.22631
machine               : AMD64
processor             : Intel64 Family 6 Model 140 Stepping 1, GenuineIntel
byteorder             : little
LC_ALL                : None
LANG                  : en_US.UTF-8
LOCALE                : English_United Kingdom.1252
pandas                : 2.3.1
numpy                 : 2.3.2
pytz                  : 2025.2
dateutil              : 2.9.0.post0
pip                   : None
Cython                : None
sphinx                : None
IPython               : None
adbc-driver-postgresql: None
adbc-driver-sqlite    : None
bs4                   : None
blosc                 : None
bottleneck            : None
dataframe-api-compat  : None
fastparquet           : None
fsspec                : None
html5lib              : None
hypothesis            : None
gcsfs                 : None
jinja2                : None
lxml.etree            : None
matplotlib            : 3.10.5
numba                 : None
numexpr               : None
odfpy                 : None
openpyxl              : 3.1.5
pandas_gbq            : None
psycopg2              : None
pymysql               : None
pyarrow               : None
pyreadstat            : None
pytest                : None
python-calamine       : None
pyxlsb                : None
s3fs                  : None
scipy                 : 1.16.1
sqlalchemy            : None
tables                : None
tabulate              : None
xarray                : None
xlrd                  : None
xlsxwriter            : None
zstandard             : None
tzdata                : 2025.2
qtpy                  : None
pyqt5                 : None