I can add a little to the points above. Basically, if we were engaged in familiar conversation with Socrates, we'd simply address him as Sōkratēs, "Socrates" – by far the most common usage in Plato's dialogues. read more
In a bit more detail, the two core elements of a personal name in (most of) classical Greece were (1) the given name and (2) the patronymic (father's name). For example, Socrates was (according to the ancient tradition) the son of a stonemason called Sophroniscus. read more
In Socrates's time thay didn't use first and last names. They were know by one name. Other examples are Aristotle, Plato and Zeus. read more
Name: Socrates . Gender: Male . Usage: Socrates, of basque origin, is a popular first name. It is more often used as a boy (male) name. People having the name Socrates are in general originating from Greece, Spain, United States of America. read more