I think there has been some kind of mix-up. Either kishi made a mistake in reflecting japaneese cultre nither we dont get something concerning japaneese culture. Just think of it. We saw the uchiha clan FULL OF MAN when madara told his story to sasuke. However, naruto's last name is after his mother kushina uzumaki, not his father minato namikaze. That means that all those MAN from uchiha clan couldnt be called uchiha, cuz they would take the last names of their mothers, like in naruto's family. But they ARE uchiha members at the same time. That means that uchiha clan members are not reletives and therefore can marry each other. But they all have the same last name which means that they are relatives. If we continue thinking in that direction we will find another mix-up. Tsunade's last name is HIME. That means that her mothers last name was HIME. That means that Tsunade's father last name was senju. Tsunade's grandfather last name was senju. That means that the wife of the first last name was senju. If we follow the logic of last names based on naruto's family, we can clearly see that the first hokage was not from the senju family. But that is impossible, cuz kishi said that he was the greatest senju ninja.
Just as I wrote at the biginning - a big mix-up.
I dont know that it has been written yet but in Japan if a woman maries to a man her name changes to her husbands, thus she gets in the clan. Naruto got his name from his mother because of protection so no 1 will know that hi is the "kyuuby boy" ( well at least not the paople out of the village )
And on the Tsunade thing we dont know what her name is... Hime means princes it is not a name but a title!