The most common name for father used in Greece today is indeed the word baba, a Turkish word, pronounced mbamba with the accent on the second syllable. It is used most often to address the father. The word patera with the accent on the second syllable, is more formal and connotes respect to the father figure.
The Greek language has borrowed many words from Turkish, such as baklava, kataifi (the popular Greek desserts), shiskebab (souvlaki), dolmades (stuffed grape leaves), etc. Besides Turkish, Greeks have borrowed words from other languages as well, such as French.