Headcanon Hell: Naruto #1
The disappearance of the Senju clan after the foundation of Konoha.
So, this issue is not addressed canonically, but it is occasionally brought up and used by fanfiction authors. I want to point out that I agree with the idea outlined by most of them, but I would like to expand it even more! (Give more details or diverge slightly.)
As an audience, we know that by the time Naruto is 12 years old, the only sufficiently famous person in the village using the Senju name is Tsunade. Tsunade, who is portrayed as a depressed woman after losing basically everyone important to her (with the exception of Shizune and, in part, her teammates).
So the narrative tells us that the clan is as good as dead.
Fandom has created a narration that its members were specifically targeted in the 1st and 2nd ninja wars because of their affinity with Hashirama and Tobirama, and that by the time Tsunade was a teenager there were only remnants left (like her brother Nawaki).
Such a rapid reduction of the clan in about 30 years seems rather unlikely to me. A great, big, clan with ‘a thousand’ different abilities - specialising in medicine - certainly wasn't sending all its members to the frontline.
So I think the disappearance of the Senju is due to how they used their surname. A lot of people replicate the headcanon that all Uchiha use Uchiha as their surname, but among themselves they use the names of different bloodlines, whose names are linked to their sharingana techniques, e.g. Uchiha Madara of Amaterasu bloodline.
In my opinion, the Senju do (did) the opposite. Their ‘thousand’ skills did not, after all, come from nowhere. I like to assume that it was due to both the absorption of smaller clans into itself and the marriage with talented individuals.
Based on how diverse they were and the fact that before Konoha was founded it was not customary to state which clan one came from, I assume that they introduced themselves in the form of a first name and surname matched to a particular bloodline, and only during missions or moments requiring proof of identity did they add of the Senju Clan. The only exception would be the main lineage. Let's make an example on the assumption that Tobirama was half Hatake and the clan recognised him as such and not just the main line: Hatake Tobirama of Senju Clan. Or based on the headcanon that Minato was related to Senju: Namikaze Minato of Senju Clan.
After Konoha was established due to cultural differences, no one paid special attention to this - after all, politics shaped the village as a Senju creation. One could say that Tobirama noticed this, only he took it as a sign that the Senju were properly integrating into the newly formed structures. Instead, he pointed out that this was not the case with the Uchiha, which is why he created the unfortunate police force.
Along with the integration process, Senju on a daily basis, in the privacy of the village's secure walls, just as in clan territory, introduced themselves using their bloodline surnames. And over time outside the village, they changed of Senju Clan to of Konoha.
The Senju name began to be linked exclusively to the main line, and here, as we know, there was actually a shortage of people. Tobirama, as far as we know, had no children. Hashirama had only 1? which produced children who remained in the clan aka Tsunade and Nawaki. (If he and Mito had more they most likely either married into other clans - maybe Akimichi and Hyuga or into Uzu or died rather early.) The only person of Senju clan portrayed as closely related to the brothers was Toka, and even here we don't know if she wasn't considered another lineage as she was a genjutsu specialist. (Perhaps she was connected to Yuhi.)
In summary, the Senju disappeared, not because there were no relatives coming from the clan, but because one, albeit, main line practically died out, and the rest assimilated to the new order.
