I understand why you can't make certain changes after a generation, but the rules do not really jive with the story, as it is supposed to be a son or daughter and not the exact same character. On that note, keeping the same name seems silly, too.
Me: Hi, I'm Runemaster, Runemaster's son, grandson to Runemaster.
Other person: Oh, you're Runemaster the Third, then?
Me: Nope.