Transforming full names to surname and initial
You are doing way too much split()-ing.  You split on ‘-‘, and if you find the length of the split is greater than 1, you split on the ‘-‘ twice more, to get the first and the second part of the hyphenated name.  Split once, and save the result in a list, and access the list elements!

You are doing too much in convertNames().  It would be better to create a convertName() method, which just processes the player name into the desired form.  Then you could call that method from convertNames().

def convertName(player):
    names = player.split(' ')

    if len(names) == 2:
        names[0:1] = names[0].split('-', 1)

    surname = min(len(names)-1, 2)

    return ' '.join(names[surname:]) + ' ' + ''.join(name[0]+'.' for name in names[:surname])

# Test data
for player in ('Novak Djorkovic', 'Jo-Wilferd Tsonga', 'Victor Estrella Burgos', 'Juan Martin Del Potro'):
    print(player, ':', convertName(player))