Originally posted by Sheep: I thought that the cognomen was separate so that when you got one of the special cognomina for doing something in the game (ie, Africanus), it would only replace the existing cognomen, not the nomen as well.
What you're describing is the agnomen, which was added onto a name due to achievments but wasn't necessarily passed down and it didn't replace the cognomen. The cognomen usually described a physical attribute e.g. Caesar-hairy, Cicero-chickpea (what an ancestor's nose looked like) and were passed down.