pd.__version__
'1.4.0.dev0+938.g1bcb84175c'

df = pd.DataFrame([[1,2],[3,4]],index = pd.Index(['a','b'],name='keepthisname'))
              0  1
keepthisname      
a             1  2
b             3  4

serc = pd.Series([5,6],name='c')
0    5
1    6
Name: c, dtype: int64

dfc = df.append(serc)  # one at a time works
              0  1
keepthisname      
a             1  2
b             3  4
c             5  6
serd = pd.Series([7,8],name='d')  # as further evidenced with this...
dfc.append(serd)
              0  1
keepthisname      
a             1  2
b             3  4
c             5  6
d             7  8

df.append([serc,serd])  # but this resets the name of the index
   0  1
a  1  2
b  3  4
c  5  6
d  7  8