Get this, Sarada is a girl. If she gets married, her son/daughter will be followed by the last name of the husband, true? So then , there will never be a Uchiha by name , only by blood - partially.
Also off-topic from my title .. Why didn't Naruto change his name to Naruto Namikaze after the 4th great ninja war? I mean , he's the strongest shinobi and world saviour. Nobody would want to try to kill him now just because he's the son of the fourth >.> <.<
None of this matters:
1. In terms of combat, an Uchiha's power comes from their genetics, not their name. In terms of social status, the name Uchiha used to bear some weight socially, but ever since the massacre, it ceases to be a formal clan, and it's not like the Uchihas were ever treated like royalty anyway. In fact, they were discriminated against. Therefore the loss of the name doesn't take anything away from anyone (whether it comes to power or social standings)
2. Naruto was first Konoha's hero after the battle with Pain, and then the world's hero after the war, and then the 7th hokage years later. The name Naruto Uzumaki and Naruto's power itself is famous and powerful enough in its own right. He doesn't need his father's name.
3. Your name is apart of you. It would be awkward to just up and change your last name just because you found out that your dad was famous. Also, why would nobody try to kill Naruto if he had the last name Namikaze, considering that plenty of people tried to kill Minato?