With pandas.DataFrame.to_csv you can write the columns and the index to a file:
import numpy as np
import pandas as pd
A = np.random.randint(0, 10, size=36).reshape(6, 6)
names = [_ for _ in 'abcdef']
df = pd.DataFrame(A, index=names, columns=names)
df.to_csv('df.csv', index=True, header=True, sep=' ')
will give you the following df.csv file:
a b c d e f
a 1 5 5 0 4 4
b 2 7 5 4 0 9
c 6 5 6 9 7 0
d 4 3 7 9 9 3
e 8 1 5 1 9 0
f 2 8 0 0 5 1