Board Thread:Wiki Discussions and Support/@comment-24971181-20141207201637/@comment-17623-20141208115646

From a past discussion, I believe it was stated that it can really depend on the clan. As the Hyuga are the most prestigious clan in Konoha, it would be more likely that Naruto married into that clan, as opposed to Hinata marrying into the Uzumaki clan.

Following this, Sai would have, in theory, married into the Yamanaka clan, and Kurai into the Akimichi clan. Meanwhile, Naruto would have married into the Hyuga, but Hinata would not have married into the Uzumaki.

The use of surnames apparently don't really matter. Hinata could go by Hinata Uzumaki or Hinata Hyuga and her connections to the Hyuga would still be the most important, while Naruto could go by Naruto Uzumaki or Naruto Hyuga.