Loss of index name when using concat function

[FANGOD]

My code

import pandas as pd


df3 = pd.DataFrame({"sip":["a","b","c","d"],"h3":[6.0,7.0,9.0,0.0]}).set_index("sip")
df4 = pd.DataFrame({"sip":["a","b","c","d"],"h3":[6.0,7.0,9.0,0.0]}).set_index("sip")
df5 = pd.DataFrame({"sip5":["a","b","c","d"],"h3":[6.0,7.0,9.0,0.0]}).set_index("sip5")
df6 = pd.DataFrame({"sip5":["a","b","d","e"],"h3":[6.0,7.0,9.0,0.0]}).set_index("sip5")
x = [df3, df4]
y = [df5, df6]

print pd.concat(x, axis=1)
      h3   h3
sip
a    6.0  6.0
b    7.0  7.0
c    9.0  9.0
d    0.0  0.0

print pd.concat(y, axis=1)
    h3   h3
a  6.0  6.0
b  7.0  7.0
c  9.0  NaN
d  0.0  9.0
e  NaN  0.0

Problem description

Y loses index name because the index of two df is different, but index's name is the same. So I think we should add a index name to df after concat. In addition, I also think that when people use concat to connect dfs with different indexes, the index and index names may be different. Of course, the index name should be consistent and better.
My use of the scene, each concat different ips table, the ip in each table may be different, when I concat, index name is None.

My solution:
1.If the index of multiple df is different, copy the index name of the first df to the df after concat, no matter whether the index of multiple df is different or the index name is different, it is feasible.
2.When the index name of conat dfs is the same, add index name.

Output of pd.show_versions()

INSTALLED VERSIONS

commit: None
python: 2.7.13.final.0
python-bits: 64
OS: Windows
OS-release: 10
machine: AMD64
processor: Intel64 Family 6 Model 58 Stepping 9, GenuineIntel
byteorder: little
LC_ALL: None
LANG: None
LOCALE: None.None

pandas: 0.20.1
pytest: 3.0.7
pip: 9.0.1
setuptools: 27.2.0
Cython: 0.25.2
numpy: 1.12.1
scipy: 0.19.0
xarray: None
IPython: 5.3.0
sphinx: 1.5.6
patsy: 0.4.1
dateutil: 2.6.0
pytz: 2017.2
blosc: None
bottleneck: 1.2.1
tables: 3.2.2
numexpr: 2.6.2
feather: None
matplotlib: 2.0.2
openpyxl: 2.4.7
xlrd: 1.0.0
xlwt: 1.2.0
xlsxwriter: 0.9.6
lxml: 3.7.3
bs4: 4.6.0
html5lib: 0.999
sqlalchemy: 1.1.9
pymysql: None
psycopg2: None
jinja2: 2.9.6
s3fs: None
pandas_gbq: None
pandas_datareader: None

[WillAyd]

Duplicate of #21629