Clarification on clan formation?

Question

On what basis were the clans formed in naruto?

The blood siblings Indra and Ashura are from different clans (Uchiha & Senju respectively)., whereas other siblings, e.g. Itachi and Sasuke are from the same clan (Uchiha).

The first shinobi who got chakra was Kaguya. So, technically whoever posesses chakra should've inherited it from her. In that case, all should be from the same clan.

Now, here's my long time doubt. How is it decided that Naruto is from the Uzumaki clan when his father is from the Namikaze family and has no clan?

Is a person's clan decided based on the abilities of the person? If yes, how is their ability evaluated right after they are born?

Answer 1

As a competing answer to the one of @MadaraUchiha, here's my take.

The clan belonging is solved quite easily. The clan-belonging is given through the generations maternally.

This means what decides the clan is not the father, but the mother. In Naruto's case that is Kushina Uzumaki

Other than that, the naruto-wiki gives some nice information:

A clan (一族, Ichizoku; Literally meaning "family"), in the loosest sense of the term, refers to a family or group of shinobi who form a basic unit of a shinobi village. Majority of these clans were mercenary military forces even before the First Shinobi World War. [...] Membership in a clan is usually determined by blood relations and genetics, which is vital in the usage of kekkei genkai and secret techniques. [...] While clans may be composed of many individuals and extended families, many clans mentioned and seen in the series were somewhat limited to a nuclear family. _{Highlighting by me}

It seems that the most clans seen, are just the mentioned nuclear families. This leads to the assumption, that one line of family that somewhen declared itself a clan is a clan. Some family lines had more offspring, and some had less. for example the Hyuuga-clan has multiple branch families, who are subordinate to the main family. The Uchiha clan on the other hand seems to just be loosely organized.

Some clans seem to have a definitive familiy head (Hyuuga, Akimichi, Nara). Other clans are not organized (Uchiha, Uzumaki, Inuzuka, [...]).

Clans mostly differ in chakra affinity and Kekkei Genkai, as well as battle style. In fact that seems to be the only thing shared in a clan. This Chakra affinity seems to be genetic, so that you are rather born into a clan than "join" it. It seems that not every person has his / her own clan, most prominent examples are probably Kakashi Hatake and Might Guy.

Answer 2

All humans came from the same ancestor ("Adam"), does that make us all family? Technically it does. Realistically, so much time had passed that no one looks at it that way.

This is the same. Based on the latest chapter, it indeed seems as though Hagoromo was the ancestor of the Uchiha and Senju clans, while Hamura (at least based on his eyes in the picture) was the ancestor of the Hyuuga clan.

That makes them all one big happy family, except that this history is long forgotten, and no one views it like that anymore.

As for clan ownership, Naruto belongs to the Uzumaki clan because his mother was from the Uzumaki clan. The Uzumaki is a subclan of the Senju, which is related to the Uchiha. Does that make Naruto an Uchiha? Not really.

Clan ownership is determined by birth, not ability.

Answer 3

All humans are not descendants of Kaguya.

Only a small amount are and they are all most all extinct i.e Uchiha, Uzumaki, Senju, Hyuga, Kaguya clans.

Answer 4

IIRC, it is not explicitly stated if you get your clan name based off the father and mother. But typically the wife would take the husbands name, for instance Hinata Uzumaki.

If you go by the principle that the wife will take the husbands name, which does not happen on a few rare occasions, it is just common sense that you'd get the fathers name, as the mother married into the clan. However, Minato is of Namikaze and Kushina is of Uzumaki, yet Naruto is named Uzumaki. Kushina never took Minato's last name because Minato had tons of enemies that sought his life and if Naruto was named Namikaze, it'd make those same people go after Naruto. Naruto wasn't named Namikaze because that would have put him in danger.

Now, for your second question.

It is correct that all chakra started from Kaguya Otsutsuki, but that does not mean that everyone should be related to her. Remember, when Kaguya had Hagoromo and Hamura, the chakra was accidentally inherited into them. Kaguya tried taking it back which eventually lead to her being sealed by Hagoromo and Hamura. Hagoromo saw chakra as not a weapon, but a power that can link everyone's soul and hearts, leading all to love each other.

Hagoromo saw chakra as a power that would bring people together, and did so by giving others chakra that did not directly inherit it from his mother, Kaguya. Because of this, clans like the Aburame and Inuzuka are most likely descendants of those Hagoromo passed chakra onto. Remember that once Hagoromo passed chakra onto others it would now become an inherited power.

Uzumaki, Senju, Uchiha, Hyuga, and Kaguya clan are all descendants of the Otsutsuki, more specifically Kaguya, and other clans such as the Inuzuka are most likely descendants of those Hagoromo passed chakra onto.