Vulcan Reforged

Yeah, Clans and then houses within those clans. I think they'd definitely want to maximize birth numbers (possibly utilizing the DNA database that Enterprise said they keep. Every Vulcan's dna sampled at birth. Security wise, I can see them keeping that backed up offworld and would be a logical way to ensure viability of clans and individual houses. They'd have access to the dna of every member born into them) so designating one child then the other to represent whatever house/clan would be a practical choice.

It's a possibility that you might see the Clans choosing to arrange inter-clan marriages between the houses so as to preserve the Clan as well. The houses seem to be more the lineage of prominent members so they might not be as tied to the preservation of those as they are the clan itself as it might not be uncommon to see those die out and be replaced by others over the generations.

Surak's house would be one of the few that would be the exception to that, but that's speculation as the only women we've ever seen marry into it, Amanda and Saavik, were without any kind of lineage on Vulcan. Amanda having no Vulcan relations and Saavik choosing not to search out hers, so there's not much to go on in terms of evidence.