I think best here is use rename with unique new columns names like:
df = pd.DataFrame({'A':list('abcdef'),
                   'B':[4,5,4,5,5,4],
                   'C':[7,8,9,4,2,3],
                   'D':[1,3,5,7,1,0],
                   'E':[5,3,6,9,2,4],
                   'F':list('aaabbb')})
print (df)
   A  B  C  D  E  F
0  a  4  7  1  5  a
1  b  5  8  3  3  a
2  c  4  9  5  6  a
3  d  5  4  7  9  b
4  e  5  2  1  2  b
5  f  4  3  0  4  b
d = dict(zip(df.columns[1::3], range(len(df.columns[1::3]))))
print (d)
{'B': 0, 'E': 1}
df = df.rename(columns=d)
print (df)
   A  0  C  D  1  F
0  a  4  7  1  5  a
1  b  5  8  3  3  a
2  c  4  9  5  6  a
3  d  5  4  7  9  b
4  e  5  2  1  2  b
5  f  4  3  0  4  b
Or:
d = dict(zip(df.columns[1::3], 
             ['name{}'.format(x) for x in range(len(df.columns[1::3]))]))
print (d)
{'B': 'name0', 'E': 'name1'}
df = df.rename(columns=d)
print (df)
   A  name0  C  D  name1  F
0  a      4  7  1      5  a
1  b      5  8  3      3  a
2  c      4  9  5      6  a
3  d      5  4  7      9  b
4  e      5  2  1      2  b
5  f      4  3  0      4  b
Not recommended solution is rename for same column names:
d = dict.fromkeys(df.columns[1::3], 'Name')
print (d)
{'B': 'Name', 'E': 'Name'}
df = df.rename(columns=d)
print (df)
   A  Name  C  D  Name  F
0  a     4  7  1     5  a
1  b     5  8  3     3  a
2  c     4  9  5     6  a
3  d     5  4  7     9  b
4  e     5  2  1     2  b
5  f     4  3  0     4  b
because if want seelct column Name it return all columns in DataFrame:
print (df['Name'])
   Name  Name
0     4     5
1     5     3
2     4     6
3     5     9
4     5     2
5     4     4