It's still going. The essence of what the family is, the genetics, is still passed on through the daughters as well as the sons. So there's that often huge pressure on guys to, "OMG j00 better start getting married now!!!111!1!!!1" just so the family name could be carried on.
Geez, it's just a name, for crying out loud.

This is why I kinda dislike family names. It's one-sided thinking, and in modern days it's easier to keep records of family lines of descent, so you almost don't need those family names anymore, at least not in sufficiently developed countries.