BUG: No longer can `melt` name the columns for the labels of a `MultiIndex`

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

frame = pd.DataFrame({("A", "a"): range(3), ("A", "b"): range(3, 6)})
frame.melt(var_name=["upper", "lower"])

Issue Description

Running the example gives

Traceback (most recent call last):
  File "<string>", line 19, in __PYTHON_EL_eval
  File "/home/jdawson/Documents/bugs/pandas-melt/melt_bug.py", line 5, in <module>
    frame.melt(var_name=["upper", "lower"])
  File "/home/jdawson/Documents/bugs/pandas-melt/.venv/lib/python3.12/site-packages/pandas/core/frame.py", line 9839, in melt
    return melt(
           ^^^^^
  File "/home/jdawson/Documents/bugs/pandas-melt/.venv/lib/python3.12/site-packages/pandas/core/reshape/melt.py", line 220, in melt
    raise ValueError(f"{var_name=} must be a scalar.")
ValueError: var_name=['upper', 'lower'] must be a scalar.

We can melt the frame if we do not supply var_name, but the columns for the labels of the MultiIndex will have the abstruse names variable_0 and variable_1.

>>> frame.melt()
  variable_0 variable_1  value
0          A          a      0
1          A          a      1
2          A          a      2
3          A          b      3
4          A          b      4
5          A          b      5

This bug may be related to #57663.

Expected Behavior

Versions strictly older than 2.2.0 behave thus.

>>> import pandas as pd
>>> frame = pd.DataFrame({("A", "a"): range(3), ("A", "b"): range(3, 6)})
>>> frame
   A   
   a  b
0  0  3
1  1  4
2  2  5
>>> frame.melt(var_name=["upper", "lower"])
  upper lower  value
0     A     a      0
1     A     a      1
2     A     a      2
3     A     b      3
4     A     b      4
5     A     b      5

Installed Versions

INSTALLED VERSIONS

commit : b552dc9
python : 3.12.2.final.0
python-bits : 64
OS : Linux
OS-release : 5.15.0-101-generic
Version : #111~20.04.1-Ubuntu SMP Mon Mar 11 15:44:43 UTC 2024
machine : x86_64
processor : x86_64
byteorder : little
LC_ALL : None
LANG : en_GB.UTF-8
LOCALE : en_GB.UTF-8

pandas : 3.0.0.dev0+618.gb552dc95c
numpy : 1.26.4
pytz : 2024.1
dateutil : 2.9.0.post0
setuptools : None
pip : 24.0
Cython : None
pytest : None
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : None
IPython : None
pandas_datareader : None
adbc-driver-postgresql: None
adbc-driver-sqlite : None
bs4 : None
bottleneck : None
fastparquet : None
fsspec : None
gcsfs : None
matplotlib : None
numba : None
numexpr : None
odfpy : None
openpyxl : None
pyarrow : None
pyreadstat : None
python-calamine : None
pyxlsb : None
s3fs : None
scipy : None
sqlalchemy : None
tables : None
tabulate : None
xarray : None
xlrd : None
zstandard : None
tzdata : 2024.1
qtpy : None
pyqt5 : None

[rob-sil]

take