Join on multi-index drops the index names when specifying "on" and "how=outer"

[wraitii]

Code Sample

import pandas as pd

df1 = pd.DataFrame(data={'i': range(0,100),'i2': range(0,100), 'u': range(200,300)}).set_index(['i','i2'])
df2 = pd.DataFrame(data={'i': range(0,100),'i2': range(0,100), 'v': range(200,300)}).set_index(['i','i2'])

ok = df1.join(df2, how="outer").head(5)
ok.index.names # ['i','i2']
bug = df1.join(df2, on=['i','i2'], how="outer").head(5)
bug.index.names # [None, None]

Problem description

When using pandas' DataFrame join function, specifying "on" with a multiple index and an outer join drops the index names. This seems buggy, as it doesn't do it on single-index or when not specifying "on" or "outer". I am not sure it's actually buggy, as in it could be by design, but it's not documented either way.

Output of pd.show_versions()

INSTALLED VERSIONS

commit: None
python: 3.6.5.final.0
python-bits: 64
OS: Darwin
OS-release: 17.7.0
machine: x86_64
processor: i386
byteorder: little
LC_ALL: None
LANG: fr_FR.UTF-8
LOCALE: fr_FR.UTF-8

pandas: 0.23.0
pytest: 3.5.1
pip: 10.0.1
setuptools: 39.1.0
Cython: 0.28.2
numpy: 1.14.3
scipy: 1.1.0
pyarrow: None
xarray: None
IPython: 6.4.0
sphinx: 1.7.4
patsy: 0.5.0
dateutil: 2.7.3
pytz: 2018.4
blosc: None
bottleneck: 1.2.1
tables: 3.4.3
numexpr: 2.6.5
feather: None
matplotlib: 2.2.2
openpyxl: 2.5.3
xlrd: 1.1.0
xlwt: 1.2.0
xlsxwriter: 1.0.4
lxml: 4.2.1
bs4: 4.6.0
html5lib: 1.0.1
sqlalchemy: 1.2.7
pymysql: None
psycopg2: 2.7.5 (dt dec pq3 ext lo64)
jinja2: 2.10
s3fs: None
fastparquet: None
pandas_gbq: None
pandas_datareader: None

[mroeschke]

I think this was fixed in the latest development cycle and will be available in the next release (0.24.0) coming soon. xref #20452

In [62]: bug = df1.join(df2, on=['i','i2'], how="outer").head(5)
    ...: bug.index.names
Out[62]: FrozenList(['i', 'i2'])

In [64]: pd.__version__
Out[64]: '0.24.0rc1+1.g33f91d8f9'