Almost nothing about you is the same as it was twenty years ago. Different cells, different beliefs, different memories, different friends. What makes you the same person across this constant turnover?
The candidates are familiar but each has a counter-example. Memory? Locke's classic answer — but memories fade and split, and false memories implant easily. Body? But your body's cells replace themselves; teleportation thought experiments suggest body might not be what matters. Continuous consciousness? You're not conscious when you're asleep, yet you wake up "the same." Some bundle of these things, woven through time? Probably — but the weaving doesn't have crisp boundaries.
Derek Parfit pushed this to a famous conclusion: "personal identity" is not what matters. What matters is psychological continuity and connectedness — and these come in degrees. A future you is "more or less you" depending on how richly connected your present mental life is to theirs. Less of you. Loose threads, not a fixed thing.
Eastern traditions (especially Buddhist) reached similar conclusions millennia earlier: the self is a process, not a substance — anatta, no-self. Whether this is liberating or terrifying depends on what you were hoping the self was in the first place.