Asian culture doesn't work like America. In Asia, women don't legally change their name to go with the husband. They can, but they don't have to, and usually don't. If a woman comes from a very prominent family, the children will take her name, or can depends on how much that's cared about. They used that in Legend of Korra. All of Suyin's children are Beifong, and her husband has her name. The Beifong family is a very famous and respected one. So Sarada can still pass on the Uchiha's name. Just like Kushina and Ino did.
Bolt and Himi got Naruto's. But Uzumaki probably trumps the Hyuuga. That or it wasn't thought they had Byakugan, so they were called Uzumaki instead. Then it may be Hanabi who will continue the Hyuga clan part of things.
But with the new-found peace, it may be possible some clans are becoming less strict. Hyashi didn't seem to mind Hinata's marriage to Naruto, since he's shown smiling at her wedding. The clan was noted to be changing.