Remember how the modern "nucular" household is largely based on a modernization of the Roman patriarchal property distribution model, where the oldest male was ascribed the identities of all members of his household, and vice versa?
That must've been extremely efficient for legal and accounting purposes, once. But, well, the only theory of mind anyone could develop in such circumstances involves grinding minds into fine paste. (There's a reason the Stoics are "seeing" an AI-driven resurgence, even though what'd be most appropriate for their target audience is probably again Skinner.)
Remember how a great deal of how we live our "personal" lives was invented in a slaveholding state which mandated belief in gods and demons. And the rest in another.
We are taught to consider all of this legacy cultural structure in terms of "haha how quaintly did people live 1000-2000-3000 years ago, were they stupid". Yet most of it lives on in some marginally altered form due to sheer global force of habit.
Take Western human naming schemes for example: does your government permit you to change your name? do you inherit one or both granddads' names? do you get a patronym? extra personal names? are you also the security force for a place, like a Freiherr de So-and-So? and at what exact number of levels of recursive self-reflection does the word "person" stop meaning the role played, and starts meaning the human playing it?
(When you're done with "identity", continue with "time-keeping" and begin to understand another psychological phenomenon causing much suffering - people's generalized inability to discern cause and effect.)
The name - the sound through which individuals are conditioned to respond to the concepts of selfhood and identity (Foobert Barber Baznix! you come here right this instant! it is not me but you who is sleepy and hungry!) - is one of many such extremely arbitrary implementation details.
Out of those emerges the thing sold to us by our caregivers and educators as "normal life" before we are able to know any better. That's the main way "primary socialization" has ever worked: a non-consensual intergenerational transmission of habits that have as much to do with self-soothing in the face of mortality as with practical concerns; in the end they just ascribe "imaginariness" to your memories of your mind being wiped, and the "you" is ready to go.
Now, in the context of all those vague and admittedly entirely hypothetical "implementation details", proceed to imagine the troop of clothed primates not as a flat list of incidental blood relations, but as a dynamic system, a living group of conscious things; if you're feeling particularly scifi - a sort of distributed organism. What would be the purpose of the scapegoat organ in that organism? Do individual primates have an equivalent organ in their bodies? (Probably not the one you're thinking of but also a valid guess)