Hi, it would be helpful to anyone considering answering here if you could specify which culture(s) or geographic region(s) you're most curious about. Meanwhile, you may be interested in these answers by /u/yodatsracist

• When did surnames become a "thing" (i.e. a hereditary legal requirement)?

As for "names" in general, that stretches deep into prehistory, so is more a question for /r/AskAnthropology or /r/AskScience (either Social Science for humans, or Biology to include answers on other species)