pandas.concat removes the name of the index column for string index columns

[AlexFuster]

Code Sample, a copy-pastable example if possible

df0=pd.DataFrame({'index':['a','b'],'foo':[1,2]}).set_index('index')
df1=pd.DataFrame({'index':['b','c'],'bar':[3,4]}).set_index('index')
pd.concat([df0,df1],axis=1)

Problem description

pandas.concat removes the name of the index column when concatenating dataframes with string typed index column, giving as a result:

	foo	bar
a	1.0	NaN
b	2.0	3.0
c	NaN	4.0

Expected Output

index	foo	bar
a	1.0	NaN
b	2.0	3.0
c	NaN	4.0

Output of pd.show_versions()

[paste the output of pd.show_versions() here below this line]
INSTALLED VERSIONS

commit: None
python: 3.6.5.final.0
python-bits: 64
OS: Linux
OS-release: 4.15.0-51-generic
machine: x86_64
processor: x86_64
byteorder: little
LC_ALL: None
LANG: en_US.UTF-8
LOCALE: en_US.UTF-8

pandas: 0.24.2
pytest: 3.5.1
pip: 18.0
setuptools: 41.0.1
Cython: 0.28.2
numpy: 1.16.3
scipy: 1.2.1
pyarrow: None
xarray: None
IPython: 6.4.0
sphinx: 1.7.4
patsy: 0.5.0
dateutil: 2.8.0
pytz: 2019.1
blosc: None
bottleneck: 1.2.1
tables: 3.4.3
numexpr: 2.6.5
feather: None
matplotlib: 3.0.3
openpyxl: 2.5.3
xlrd: 1.2.0
xlwt: 1.3.0
xlsxwriter: 1.0.4
lxml.etree: 4.2.1
bs4: 4.6.0
html5lib: 1.0.1
sqlalchemy: 1.2.7
pymysql: 0.9.2
psycopg2: None
jinja2: 2.10
s3fs: None
fastparquet: None
pandas_gbq: None
pandas_datareader: None
gcsfs: None

[WillAyd]

Thanks for the report but closing as a duplicate of #21629