Changes by family. The Stones have some kind of gem name or a name that means rock or stone at least once per generation, leading to names like Amber Gemma, Jewel, Ruby, Peter, Pedro
The Yomins. Well, it's Nimoy backward, and they're aliens. I'm trying to see how long I can keep giving them the names of actors and actresses who played Vulcans. Into Generation 4, that's still working. And no, the founder was not named Leonard, though that was tempting, and ended up being used for a descendant.
The Davids tend to get Hebrew names, as long as I like them.
The KIbos alternate between Japanese and whatever name I happen to like that day.
Think the random legacy family won't have a particular theme, because it's random after all.