Some philosophers think that every time you lose your train of thought (e.g. zoning out while driving or falling asleep) your consciousness disappears and a new consciosness forms later when you "snap back" (or wake up). This new consciousness shares only memories and personality with the previous one, but it is otherwise a new entity, similar to the teleporter thought experiment.

Conveniently, this makes death less scary.

Further reading: Zen and the Art of Consciousness by Susan Blackmore

I think what I was getting at is that it may be impossible to tell from the outside if something is conscious or not. If I can't even prove to myself that another person is conscious, I might have a hard time proving that a computer is conscious.

That is an interesting thought.

It might depend on how you define "person". When I look around, I see distinct human bodies. When I wake up, I'm in the same body as when I went to sleep, so in that sense I'm the same person.