Naruto and Hinata's third child: Main or Second branch of Hyuga?

[chaos control]

I think that only applies when both parents are from clans of the same social level. (Uzumaki is as prestigious as Senju, Hyuuga and Uchiha). If Sasuke was a Haruno and Sakura an Uchiha then his kids would have inherited the Uchiha name.

And IMO Bolt should be an Uzumaki considering the clan's almost extinct, and that would also add a parallel to Sarada who has to rebuild Uchiha clan.

I have to disagree for a certain reason. Naruto got the name Uzumaki only because Hiruzen wanted to protect Naruto from Minato's enemies. Otherwise he would have been Naruto Namikaze (despite the fact that the Uzumaki clan has more prestige than the unheard of Namikaze family).