Usually, any character adopts his/her name according to their father’s clan in the Japanese anime industry. Now you may ask- why is Naruto Uzumaki and not Namikaze? Well, he had his own valid reasons and he didn’t have any choices to make actually.
To save Naruto from his father’s enemies, the third hokage gave Naruto his mother’s identity. After his parents death, many ninjas from far away villages would come to slaughter the rest of the relatives of Minato Namikaze- Naruto’s Father.
What Happened During the Third Shinobi War?
During the war, Naruto’s father, the fourth Hokage of Konohagakure, killed 1000 Shinobi. His fierce actions were feared by people at that time. So, he actually stopped the war from going any worse and forced clans to maintain peace.
But in the process of being the Yellow Flash (deadly ninja), he made few enemies. They always waited for a chance to kill his entire clan so that they could have the powers to themselves. And they got their chance during the Nine-Tailed Fox incident.
Aftermath of Naruto’s Parents Death:
Naruto’s parents died while saving the new born baby and the whole village. And the third Hokage, Hiruzen Sarutobi, started taking care of the kid. Although he never actually cared about Naruto’s upbringing, he gave him the surname of his mother’s to hide his identity from enemies.
Even Naruto didn’t know about his parent’s unfortunate fate in his early childhood. But after hearing the story behind his parents’ sacrifices, he immediately vowed to be the strongest Ninja of Konoha and served the people throughout his life.
Another theory that roams around the internet is that Minato Namikaze was an orphan since childhood and his clan Namikaze didn’t have any prominent power or interest in Jutsu. Therefore, when he married Kushina, he took her surname because many strong shinobi and ninja belonged to the clan.
But in my opinion, that could hurt both Namikaze and Uzumaki clan after the nine tailed fox incident. And only the Namikaze clan members were killed because they were thought to be as deadly as Minato.
The reason behind the doubt- ‘why is Naruto Uzumaki and not Namikaze’ was to maintain Naruto’s safety one way or another. None of the villagers actually loved him because their beloved hokage died while saving him. So, there was only one way to save the child by hiding his real identity.