This got me thinking, if your consciousness and body were cloned, but your cl9ne ended up in a different place than you, the one that started as a copy would gain new memories, so when you eventually met, you two would be different. I know this isn’t quite what you were think9ng but it made me think of that
Your situation is a fairly used trope. "Thomas" Riker in Star Trek is one that you might have heard of (a Transporter accident, of course... I'm amazed they ever work correctly).
There's a book I got from a discount/remaindered book store a few years ago (must not have sold as well as hoped in regular outlets) where the whole thing about the galaxy was various different 'cloning' methods. Main protagonist is a (slightly imperfect) clone created from a hard-copy record of his bodyplan (to atomic level detail) that some mysterious aliens found floating in space. Blown up and smashed but (
almost entirely) reconstructable. If you have patience to scour the vicinity for the fragments and enough additional patience to piece it back together. Then decode it, and use that information to reconstruct the person they discover it encoded. That's basically the set-up, and now we have this 'clone', a veteran of many an intragalactic military action, no knowledge of how 'he' got encoded and why the encoding got 'destroyed' setting off to solve his own mystery.
Fairly soon (n.b. 'soon' is relative, there's no proper FTL, the galaxy is a big place, the societies in it work with that limitation, including the ones who share single consciousness between different bodies dotted many thousands of LY apart, "left hand not (yet) knowing what the right hand is doing" is one way to describe it) he reunites with his old squad, whose individuals seem to embrace their own unique way of living in this clone-heavy technosociety. One of them seems to prefer duplicating himself, letting all copies wander around for years at a time then, when two versions meet up they go into a room,
something is decided between himselves, one of him leaves the room with the combined experiences of himself now reunited in the only surving body of the pair.
Almost the opposite, a much older book I once read features a 'side-effect' of teleportation being exploited. Normally the source-body would be destroyed in order that the destination body would be the only extant one. If it is not, there's moments of confusion as the experiences of the two selves (seemingly 'linked' in a quantum/soul manner) vie to be experienced by both selves at once. However, if you teleport whilst in a sensory deprivation chamber then the link remains one version (the copy) can go and do something very dangerous and ultimately fatal, at which point the consciousness in the 'home' version survives but with memories of how the copy died. Which was very important in the plot of this book (it requires exploration of an impossibly booby-trapped alien ship/artefact, where it's useful to know exactly how you died last time, each time you get your copy sent into it again) though needed something of a unique mental attitude to tolerate being subjected to such death/resurrection.
Of course, that's all fiction. Made to satisfy plot needs. In lieu of practical apllication and study, either of cloning or (sufficient) AI, it's more hypothetical philosophy than any natural philosophy.