Board Thread:Theories and Speculation/@comment-28550406-20160601140633/@comment-3965545-20160601202924

The only reason Naruto kept the Uzumaki name was in order to keep Minato's enemies from getting to him. Otherwise the women take the males surnames in Naruto(except for Sai for obvious reasons) so if her father was Hashi's son she would be Senju, if not then her last name could be any other clan name, you'll never know.