text: Title: BUG: pd.Series.rename(..., inplace=True) returns a pd.Series and not nont
  Body: ### Pandas version checks
  
  - [x] I have checked that this issue has not already been reported.
  
  - [x] I have confirmed this bug exists on the [latest version](https://pandas.pydata.org/docs/whatsnew/index.html) of pandas.
  
  - [x] I have confirmed this bug exists on the [main branch](https://pandas.pydata.org/docs/dev/getting_started/install.html#installing-the-development-version-of-pandas) of pandas.
  
  
  ### Reproducible Example
  
  ```python
  In [1]: import pandas as pd
  
  In [2]: pd.Series([1, 2, 3])
  Out[2]:
  0    1
  1    2
  2    3
  dtype: int64
  
  In [3]: pd.Series([1, 2, 3]).rename('A')
  Out[3]:
  0    1
  1    2
  2    3
  Name: A, dtype: int64
  
  In [4]: pd.Series([1, 2, 3]).rename('A', inplace=True). # should return None
  Out[4]:
  0    1
  1    2
  2    3
  Name: A, dtype: int64
  ```
  
  ### Issue Description
  
  According to the [documation](https://pandas.pydata.org/docs/dev/reference/api/pandas.Series.rename.html), inplace operations should return None and only modify the object in place without doing a deepcopy.
  However when running the rename operation on `pd.Series` with `inplace=True` the type of the returns is `pd.Series` and not None.
  This seems to originate from quick look up in the `_set_name` operations that return and object no matter the value of `inplace` (cf https://github.com/pandas-dev/pandas/blob/6bcd30397d67c3887288c7a82c2c235ce8bc3c7f/pandas/core/series.py#L1835-L1850).
  And then the `rename` operation only returns the result of `_set_name` without distinguishing the `inplace` value.
  
  ### Expected Behavior
  
  The docs suggest that the return of the `rename(..., inplace=True)` should be None.
  
  ### Installed Versions
  
  <details>
  
  INSTALLED VERSIONS
  ------------------
  commit                : 0691c5cf90477d3503834d983f69350f250a6ff7
  python                : 3.13.1
  python-bits           : 64
  OS                    : Darwin
  OS-release            : 24.3.0
  Version               : Darwin Kernel Version 24.3.0: Thu Jan  2 20:24:06 PST 2025; root:xnu-11215.81.4~3/RELEASE_ARM64_T8103
  machine               : arm64
  processor             : arm
  byteorder             : little
  LC_ALL                : None
  LANG                  : en_US.UTF-8
  LOCALE                : en_US.UTF-8
  
  pandas                : 2.2.3
  numpy                 : 2.1.3
  pytz                  : 2024.2
  dateutil              : 2.9.0.post0
  pip                   : 24.3.1
  Cython                : None
  sphinx                : None
  IPython               : 8.29.0
  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            : 3.9.2
  numba                 : None
  numexpr               : None
  odfpy                 : None
  openpyxl              : None
  pandas_gbq            : None
  psycopg2              : None
  pymysql               : None
  pyarrow               : None
  pyreadstat            : None
  pytest                : 8.3.3
  python-calamine       : None
  pyxlsb                : None
  s3fs                  : None
  scipy                 : None
  sqlalchemy            : None
  tables                : None
  tabulate              : None
  xarray                : None
  xlrd                  : None
  xlsxwriter            : None
  zstandard             : None
  tzdata                : 2024.2
  qtpy                  : None
  pyqt5                 : None
  
  </details>
  