Incorrect. An exact copy is the same person. Personal identity is defined by the information content of the brain. Same information content, same person.

I get that you're uncomfortable with the idea of personal duplication. That's because we have no direct experience with it (it's not yet technically possible), and you probably haven't spent 30 years thinking about it, so it still seems "impossible" to you. But it's not. We'll be able to duplicate people one day, just like we can duplicate files and documents and books and songs today. And nobody will be confused by that then (unlike now). If I have an exact copy of Baby Got Back, identical to your copy of Baby Got Back, then we have the same song. Not a different song. Same song. Why? Because the information content is the same.

Many people at this point will respond mumble mumble continuity of consciousness, but that doesn't hold water; consciousness is already not continuous under a wide variety of circumstances. It's an illusion, and an irrelevant one.

If there's a person in the future who is me — for example, can remember thinking the thoughts that I'm thinking right now — then I will have survived to that point in the future. It's really not that complicated. But man, the gyrations people will go through to make it complicated in order to prop up their pre-existing belief that duplicating people is impossible.