I don't think I've seen the name change due to marriage. I suspect the Spanish kind of patrilineal last name system or something like that would be adopted quite a bit more in a world like this, both because you have two parts so more identification points and because people's names stay.

But if names adjust to their current state and there was a family name system that opens interesting possibilities, like say a couple has their first kid out of wedlock, so first it gets the mother's maiden name, and if their soulmate is born and shows it they get that. But then the couple marries and the kid gets a different family name...

Also the depressing scenario when your soulmate's name changes to a religious name because they became a monk or a nun. Though maybe they wouldn't do celibacy in that kind of universe. Actually I don't think I've ever seen a soulmate fic address that, i.e. whether in that universe say the Catholic church demands its priests to be with their soulmate only platonically.