Why is Namikaze Minato not the whirlpool Watergate in Naruto?

He doesn't belong to the Xuan clan. Everyone in that family has red hair, and Namikaze Minato is Namikaze Minato. Uzumaki Kushina belongs to the Whirlpool family. Naruto wants to protect his own safety, so the name of Naruto in the third generation is Naruto Uzumaki. If Naruto and Watergate have the same surname, he will look for attacks from other villages or expose Kyubi no Youko on him.