I think people still do it. It's just harder to do given all the legalities of it. If I didn't like my family name, I'd change it. I wonder if we'd choose professions now, given the choice, or something else.

Kind of related, but my last name is "Kousha" which means "hard worker" in Persian. (I didn't learn this until I was 30.)

Everyone would call my Persian grandfather "engineer" rather than by his first name and despite him not being college educated.