The combination of four columns in two.

[michalmonday]

Possibly it would be good idea to remove duplicates (where the same name has the same number)

import pandas as pd
#import numpy as np

df = pd.read_csv('telephone_calls.csv')

names = list(df[['Name1','Name2']].unstack())
numbers = list(df[['Telephone1','Telephone2']].unstack())
# alternative: df['col_1'].append(df['col_2'], ignore_index=True)

for name, num in zip(names, numbers):
    print(name, num)

Output:
Alice 085 646 4923
Derek 082 467 5217
Derek 082 467 5217
Benjamin 084 614 6635
David 084 852 1646
...

Edit:
If you'd like to keep working on dataframe you could use something like:

import pandas as pd
#import numpy as np

df = pd.read_csv('telephone_calls.csv')

names = df['Name1'].append(df['Name2'], ignore_index=True)
numbers = df['Telephone1'].append(df['Telephone2'], ignore_index=True)

new_df = pd.DataFrame({'Names' : names, 'Numbers': numbers})
print(new_df)

# alternatively:
# new_df = pd.concat([names, numbers], axis=1, keys=['Names', 'Numbers'])

Output:
       Names       Numbers
0      Alice  085 646 4923
1      Derek  082 467 5217
2      Derek  082 467 5217
3   Benjamin  084 614 6635
4      David  084 852 1646
...