There is no "I" in "You"

[Aoi Magi]

Yes

By what method(s) do you presume to know or question A's self-identity?

A's non-existence at the point of C's existence would be a start...

Moreover, A can choose self-identify as B even without that merger, relying solely on one's self-identity is a bit pointless.

But looking at it from another perspective, if we are to take A's view of self-identity as truth then it'd mean just the experiences or memories make an individual, but in that case none of A or B's relatives or friends would have memories or experiences of this ((A+B)/2) person and for them it'd be a person similar or quite like the person they knew but not that exact same individual.