Personally, I find this particular thread funny because in the beginning, I too thought the same thing, with usually the child always inheriting the father's surname, however, looking at it from a logical point of view, I see now why it is 'Uzumaki' and not 'Namikaze'
One reason is because if anyone were to say the fourth Hokage's full name, then Naruto would instantly know now he is related to the fourth Hokage without finding out later like he should according to the story plot. I feel 'Uzumaki' was placed their for 'protection' of Naruto and his family identity. In the begining, it was given off to the viewers that Naruto's father was indeed, Minato, but Naruto himself did not know. I feel Kishi did that in order to keep Naruto oblivious to the fact he had some blood relation to the Fourth Hokage himself.
That and for the other numerous reason's 'Uzumaki' was given to him. It became a fitting pun to the show's main hero himself as he is named Naruto for the swirls in the Ramen, and the swirl of the Uzumaki clan relating to that symbol that identifies with Naruto. The last name 'Uzumaki' also relates to the fact of his 'Rasengan' is the wind element that swirls in tbe same fashion the Uzumaki symbol is formed, giving another little pun to his character. Imo, the last reason for this is because there really isn't anymore true 'Uzumaki's' around besides Nagato (desceased now) and Karin. Perhaps Kishi wanted to also give his character, the underdog, the name as he would be the greatest example of an Uzumaki who is still around, despite the fact he is not full-blooded.
Personally, as cool as 'Namikaze' sounds, 'Uzumaki' just has the ring to it that we all are used to by now and probably would be hard for most fans to see thim with the surname change. Who knows? Maybe after seeing his dad again on the battlefield he will have a change of heart and finally take his father's surname. Not likley, but just a thought lol
What I mostly meant was that AFTER Naruto learned that he was the Yondaime's son, it would have been logical to change his name to Namikaze, especially since the reason for giving him his mother's name (protection against his father's enemies) is null because Naruto is now able to protect himself.
