Rename Dataframe column based on column index

@MaxU's answer is better

df.rename(columns={"col1": "New name"})

More in docs

UPDATE: thanks to @Vincenzzzochi:

In [138]: df.rename(columns={df.columns[1]: 'new'})
Out[138]:
   a  new  c
0  1    3  5
1  2    4  6

In [140]: df
Out[140]:
   a  b  c
0  1  3  5
1  2  4  6

or bit more flexible:

In [141]: mapping = {df.columns[0]:'new0', df.columns[1]: 'new1'}

In [142]: df.rename(columns=mapping)
Out[142]:
   new0  new1  c
0     1     3  5
1     2     4  6