The transporter paradox questions whether Captain Kirk on the ship is the same person as Captain Kirk once he beams down to a planet. Sure, he has the same molecular structure, the same brain in the same state as when he departed, but there is energy loss, and we know that at a small enough scale planet Kirk is not rebuilt exactly as ship Kirk was taken apart. Is it the same guy, or two different identical guys? (It gets worse when Picard dies and is reassembled from transporter memories and nobody talks about that incident ever. )

Don't forgot the time when Riker was beamed up off a planet during some weird EM storm and the interference caused him to be reconstituted both on the ship and on the planet, resulting in a ship Riker who went on with his Starfleet career and a planet Riker who spent years trapped on an uninhabited, ruined planet waiting for a rescue that never came because they were completely unaware he even existed.