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Description
Pandas version checks
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-  I have confirmed this bug exists on the latest version of pandas. 
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Reproducible Example
import pandas as pd pd.Index([], name=True).get_level_values(level=True)Issue Description
I get IndexError: Too many levels: Index has only 1 level, not 2. Also,  pd.Index([], name=True).get_level_values(level=False) should raise KeyError, but it returns the whole index.
Also, name np.nan, pd.NA or pd.NaT causes  KeyError: 'Requested level (nan) does not match index name (nan)'.
Expected Behavior
I should get the whole index from get_level_values(True)
Installed Versions
commit : 4665c10
 python : 3.13.5
 python-bits : 64
 OS : Darwin
 OS-release : 24.6.0
 Version : Darwin Kernel Version 24.6.0: Mon Jul 14 11:30:30 PDT 2025; root:xnu-11417.140.69~1/RELEASE_ARM64_T6020
 machine : arm64
 processor : arm
 byteorder : little
 LC_ALL : None
 LANG : en_US.UTF-8
 LOCALE : en_US.UTF-8
pandas : 2.3.2
 numpy : 2.3.2
 pytz : 2025.2
 dateutil : 2.9.0.post0
 pip : 25.1
 Cython : None
 sphinx : None
 IPython : 9.4.0
 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 : None
 numba : None
 numexpr : None
 odfpy : None
 openpyxl : None
 pandas_gbq : None
 psycopg2 : None
 pymysql : None
 pyarrow : None
 pyreadstat : None
 pytest : None
 python-calamine : None
 pyxlsb : None
 s3fs : None
 scipy : None
 sqlalchemy : None
 tables : None
 tabulate : None
 xarray : None
 xlrd : None
 xlsxwriter : None
 zstandard : None
 tzdata : 2025.2
 qtpy : None
 pyqt5 : None