edited to add that this is during the warring clans era, pre-Konoha, just realised I didnt necessarily make that clear enough throughout the post oops
anyway
concept: the real reason Tobirama wears his big fur ruff, or at least one of the main reasons he wears it so consistently, is to hide the collar he refuses to take off. Izuna gifted it to him and Tobirama doesn't want to remove it but it's not exactly SUBTLE (uchiwa fan symbol, writing which reads "property of Uchiha Izuna") so if he wants to wear it without immediately getting murdered for treason he kind of has to hide it. and he DOES want to wear it. thus, the big fur ruff which he can conveniently blame on being important to him due to his summons and/or Hatake heritage, so nobody questions it, and which hides his collar from view (Izuna absolutely knows why he's wearing the fur and the knowledge that his Senju is taking such a risk just to wear the collar Izuna gifted drives him a little insane)
different flavour of the same concept: Izuna didn't GIFT it to Tobirama, but INFLICTED IT on him. Izuna thinks it's the greatest thing he's ever done and is maddeningly smug about it but fortunately, or unfortunately depending on whose perspective you're considering things through, he can rarely ever SHOW that smugness or gloat about it without others catching on that he collared Tobirama. And he doesn't want that. Tobirama, meanwhile, has repeatedly tried to remove the collar and failed. He was pissed off when Izuna first got it on him, got steadily more annoyed when his first several attempts to remove it whilst on his way home from the mission/battle Izuna had caught him on failed, and reaches incandescently furious when he finally gets a mirror and sees exactly what he's been branded as. He probably broke the mirror actually once he realised the collar he can't figure out how to remove declares that Izuna OWNS HIM how dare he-
After that point Tobirama definitely puts even more effort and fury into trying to kill Izuna, and possibly spreads that fury to other Uchiha as well which is partly emotions getting the best of him and partly his assumption that surely Izuna couldn't have come up with something impossible to remove himself and therefore there must be at least ONE accomplice. There we go, secret behind Tobirama's hatred for the Uchiha unveiled: Izuna massively overstepped and Tobirama will hold this grudge until the end of time, against everyone even mildly associated with Izuna
optional add-on, for either version of the concept: the writing on the collar is actually in Sharingan code (if you haven't seen that concept around before, idk if it's canon or fanon but basically it's writing that you can only read with active Sharingan, otherwise it's just decorative looking squiggles), and the uchiwa symbol is on the BACK of the collar. This means that dependent on exactly how long Tobirama's hair is vs how high or low the collar sits on his neck, and/or how careful he is about nobody getting a look at the back of his neck, he could actually openly wear the collar around any non-Uchiha without getting accused of treason (though if he's wearing it involuntarily he probably wouldn't want to). Though "not getting accused of treason against the Senju" would not save him from "judgement for wearing a collar with fancy attention-grabbing squiggles". Also, what would happen if he wasn't covering the collar (thru choice or bc he lost his fur or whatever) on a mission and then - whoops. That's a Uchiha. That's a non-Izuna Uchiha. That's a non-Izuna Uchiha with sharingan currently active and looking in this direction and- ah fuck please say they can't read the writing at this distance-
another optional add-on, for any of the above: I couldn't decide when initially thinking about this if the collar should be JUST a claim or if other bullshit is going on. So the optional add-on is: Izuna gifts/inflicts on Tobirama a collar when they're both younger, like pre-teens or smth, which is nothing except a claim. Later when Tobirama inevitably outgrows that collar, Izuna has another one ready with the same visible claim, but also has seals stitched in - may or may not actually be visible when looking at it, Izuna may or may not bother telling Tobirama about them. Of course Tobirama would be significantly more upset about this in the "get this fucking thing off me I hate you how dare you" version of the initial concept than the "yesss gift thank you I'm never taking it off" version,,,,but I'll leave it up to you to decide exactly what functions Izuna includes in the collar, because otherwise I'm going to be sat here indecisively chasing different versions of it for like, hours. Although I think in the "gift" version, Tobirama may also add his own seals to it
