The ship of Theseus

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Watching a sci-fi show involving personalities switching bodies, it occurs to me that things like the ship of Theseus problem occur when we are dealing with conventionally delimited entities, such as "Jim's car." The car has no intrinsic metaphysical connection to Jim; it is only his by the ownership conventions of the society he lives in. But in these sci-fi scenarios where X's memories are "implanted" into Y's body, and X is in a coma or something, the question is not answered by any "closest continuer" criterion or anything like that: persons are metaphysically distinct entities, and the answer to "Who is really X now?" is just the answer to, "Well, where is X now?" (Not to claim that is easy to answer.)

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