BUG: Rename with dict argument on axis=0 gives incorrect result

[sfc-gh-joshi]

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Reproducible Example

import modin.pandas as pd
df = pd.DataFrame([[0] * 3] * 3)
df.rename({0: "a", 1: "b", 2: "c"})

Issue Description

When a dict is passed to DataFrame.rename, the entries represent mappings to update the index (if axis=0) or column labels (if axis=1).

The above code is a no-op in current modin, but with native pandas updates the row labels like so:

>>> df.modin.to_pandas().rename({0: "a", 1: "b", 2: "c"})
   0  1  2
a  0  0  0
b  0  0  0
c  0  0  0

Note that modin has correct behavior for axis=1.

Expected Behavior

The row labels should be updated, as with native pandas.

Error Logs

N/A

Installed Versions

INSTALLED VERSIONS

commit : c046a92
python : 3.9.21
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

Modin dependencies

modin : 0.35.0+4.gc046a92a
ray : 2.49.1
dask : None
distributed : None

pandas dependencies

pandas : 2.3.2
numpy : 2.0.2
pytz : 2025.2
dateutil : 2.9.0.post0
pip : 25.2
Cython : None
sphinx : 5.0.2
IPython : 8.18.1
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : 4.13.4
blosc : None
bottleneck : None
dataframe-api-compat : None
fastparquet : None
fsspec : 2025.9.0
html5lib : None
hypothesis : None
gcsfs : None
jinja2 : 3.1.5
lxml.etree : 5.3.1
matplotlib : 3.9.4
numba : 0.60.0
numexpr : None
odfpy : None
openpyxl : 3.1.5
pandas_gbq : None
psycopg2 : None
pymysql : None
pyarrow : 18.1.0
pyreadstat : None
pytest : 7.4.4
python-calamine : None
pyxlsb : None
s3fs : 2025.9.0
scipy : 1.13.1
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
xlsxwriter : None
zstandard : None
tzdata : 2025.2
qtpy : None
pyqt5 : None