Did people have surnames 2000 years ago?

Answer 1

Not in the same hereditary way as the current practice in Western society. In some cultures right up to today, the same could be said.

So many of our surnames today have derived from the older practices. Hebrews used Ben to indicate "son of - ", as in the movie Ben Hur. The protagonist is Judah Ben Hur, Judah the son of Hur (Hur being a man's name). A read through The Bible will show a variety of practices from 2000 years ago and earlier.

Of more recent times the Scottish "Mac -" is another "son of - " prefix. MacPherson = son of the parson etc. English names like Cutler (a person who makes cutlery), Baker (a baker), Cooper (a barrel maker), Fletcher (an arrow maker) etc etc etc obviously come from the person's work.

Such practices seem to have been used down through history - in fact it would be hard not to use the practice even if not formalised.