Or it's possible that there's some complicated formula, where the lower status person joins the higher status clan, or maybe if its an eldest child marrying a younger child, they join the eldest child's house, or things like that.

...Okay, now I'm thinking about Spock. Who, when he was betrothed to T'Pring, was a younger son, because Sybok hadn't been cast out yet iirc. So, what if everyone was expecting him to join T'Pring's clan, and then Sybok is cast out and all of a sudden Spock is an only son, so she would have to leave her own clan to join his. Which, if she's not that thrilled with the idea of marrying him to begin with, is just salt in the wound. Put her not wanting to be "the consort of a legend" in that context ... there's a story there. Which I Am Not Writing, because I have too much else to do.

(but I want the story about T'Pau adopting Amanda, and how that stuff works out post-Reboot, as well, please write it!)