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.