Look this is the old Greek philosophical question of The Ship of Theseus, or a Soroites paradox.
One explanation for who we are is that experience is a binary relation. In order for identity or anything else to be experienced by someone, they have to be operating.
There is an episode in Star Trek where a transporter accident didn't destroy the original copy. Obviously a copy of someone isn't that someone because identity is a transitive relation, and the two copies aren't each other!
So by simple logic, a copy of someone isn't that someone because you can have multiple copies. Of course the real issue is the question of someone's identity in the first place.
Because identity is a TRANSITIVE relation (meaning if A is related to B and B to C then A is related to C). And two copies of the same thing aren't each other.
Actually identity is an example of what's called an EQUIVALENCE RELATION which means it is reflexive (A is related to A), SYMMETRIC (If A related to B then B related to A) and transitive. Those 3 properties are necessary and sufficien for a relation to be an equivalence relation. An equivalence relation partitions a set into subsets called "equivalence classes" where all members are equivalent.
So the big question is, what is the relation here that would form equivalence classes between copies of a person? Perhaps it is that two people are the same if, in some sense, they arose as a natural continuous change from some previous biological thing.
That way we can acknowledge the vast complexity of what it's like to be human and alive, and still make a meaningful definition.
It just so happens that this definition is along the lines of hinduism - I've been listening to some Alan Watts lecture recently.