Throughout history, ancient Greeks did not have official last names, but they did have some patronymic characteristics (i.e., Achilles was Achilles Pileidis from his father Pileas).
“Patronymics” means that Greek surnames usually come from the first name of the father of the family. So if someone’s last name is Demetriou, that means that the surname came from a man named Demetrios.
The matronymic names refer to those that cane from the mothers’ name, the national or toponymic names refer to surnames created by names of towns or districts. There are also Greek surnames referring to a profession, or the paronymic ones, referring to different abilities, or even animals.
Until a few years ago, women took their husband’s surname. Eventually, they were able to keep both surnames. Today, they are free to choose whether they want to keep their surname or add the one of their husband.
Some of the most common Greek surnames you can find include Papadopoulos, Papadakis, Ioannou, Georgiou and Demetriou.