In Jewish tradition, even today, a man's full name is, for example, Isaac ben Abraham, where "ben" means son of. And a woman's name would be Rebecca bat Bethuel, where "bat" means daughter. In both cases, the father's name, not the mother's is given.
And, as noted in other comments, people are also identified by a first name plus a home town (Jesus of Nazareth) or an epithet describing something that the person had done, or was famous for, such as Thomas Didymus (Thomas the Twin), or James the Greater and James the lesser.
Today, in public prayers for healing in the synagogue, people are called by their given name, and then son or daughter of their mother's name.