That's just a rewording of the ancient Theseus's paradox. It doesn't matter, there is no correct answer so whatever answer you choose is correct.
I swear every time I come up with a new idea I find out that people have been thinking about it for millennia. lol
Although I disagree that it doesn't matter. If you and future you aren't the same person, then it's a huge shift in many areas of philosophy. For example, if it's true than ethical egoists should logically be shortsighted about their decisions.
It also greatly changes the relation that we have with death and immortality. If me 20 years in the future is not me then it means that in a way I will be dead in 20 years and the person there will only be an echo. It also completely negate the possibility immortality as traditionally understood as if medicine somehow manages to completely reverse aging, we would still not be immortal. Rather, our immortal body would be like an infinite echo hosting an infinite number of different persons.
This assumes that you can take a snapshot of someone tens of years apart while ignoring everything that happens in between. Yes, if you just pulled out a new copy body out of your ass, I'd agree that it is not the same person. However, in reality, the process of change is constant and gradual. With every new step, there's something else added to the list, and something taken out. If we assume that just a single one newly acquired atom is to be a part of you, then every atom acquired one at a time is also you. There is no jump in your composition, so you are always you. Even if by the end nothing of the original you remains.
There's also a problem of the soul, if one chooses to believe in it, that makes the argument moot. As it is the soul that ascribes identity, not the body and the body's composition is a moot point.
