BUG: Interchange protocol implementation allows non-string column names

[stinodego]

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 pandas as pd

df = pd.Series([1, 2, 3], name=0).to_frame()
names = df.__dataframe__().column_names()
for n in names:
    print(type(n))
# <class 'int'>

Issue Description

The spec requires that column_names returns an Iterable[str]. This is currently not the case.

Expected Behavior

The names should be converted to strings when yielding them in the column_names method.
Perhaps the original names can be stored in the metadata field, in order to preserve the original type on a roundtrip.

@MarcoGorelli another one ;)

Installed Versions

commit : a671b5a
python : 3.12.0.final.0
python-bits : 64
OS : Linux
OS-release : 5.15.133.1-microsoft-standard-WSL2
Version : #1 SMP Thu Oct 5 21:02:42 UTC 2023
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_US.UTF-8
LOCALE : en_US.UTF-8

pandas : 2.1.4
numpy : 1.26.2
pytz : 2023.3.post1
dateutil : 2.8.2
setuptools : 68.2.2
pip : 23.3.2
Cython : None
pytest : 7.4.0
hypothesis : 6.92.1
sphinx : 7.2.4
blosc : None
feather : None
xlsxwriter : 3.1.9
lxml.etree : 4.9.4
html5lib : 1.1
pymysql : None
psycopg2 : None
jinja2 : 3.1.2
IPython : 8.18.1
pandas_datareader : None
bs4 : 4.12.2
bottleneck : None
dataframe-api-compat: None
fastparquet : None
fsspec : 2023.12.2
gcsfs : None
matplotlib : 3.8.2
numba : None
numexpr : None
odfpy : None
openpyxl : 3.1.2
pandas_gbq : None
pyarrow : 14.0.2
pyreadstat : None
pyxlsb : 1.0.10
s3fs : 2023.12.2
scipy : None
sqlalchemy : 2.0.24
tables : None
tabulate : 0.9.0
xarray : None
xlrd : None
zstandard : 0.22.0
tzdata : 2023.3
qtpy : None
pyqt5 : None

[neha3004]

Can you assign this issue to me?