I can't understand how come Naruto's surname was chosen to be Uzumaki, because, if they were to hide Naruto's relation to Minato, they couldn't choose Minato's wife surname, for she was the only Uzumaki left in the Leaf village. So, Hiruzen had to give a plausible justification for why Naruto's surname would be Uzumaki, once he was supposed to be just an ordinary kid. So, what do you think of the theory of Naruto's surname Uzumaki being chosen by Hiruzen on the grounds of honoring the Uzumaki clan? After all, they had lost their last member, Kushina (at least in the Leaf village), and they were very close to the village. This way, Hiruzen would hide Naruto's relation to Minato, by not giving him the Namikaze surname, and would hide Naruto's relation to Kushina (and, hence, to Minato), because ordinary people would think Naruto was a random orphan who wasn't actually a member of the Uzumaki clan, for his surname would be just symbolic (for them). But, in the other hand, Hiruzen would successfully preserve Naruto's surname (Uzumaki) for when the time he would find out the truth arrived.