No, because you also change with time. You from today are slightly different than what you are yesterday, and you from a second from now will be slightly different from you from right now, because your thinking requires the patterns in your brain to change, just a little. If you copy yourself, both of you will experience different things, and dont have a means to sync those different inputs between you, and so you immediately diverge into two separate if similar entities. Youre both equally a progression of the original and so both are that original person in the same way that you as an adult and you as a kid are the same person, but once diverged youre no longer the same person as eachother. If the teleporter destroys the original while scanning them and then recreates them, theres only ever one of you at once. You only get an issue if you make the copy before destroying the original, because then there are experiences formed after the scanning process, and that new version of the identity is lost.

A bit like how theres a notion you sometimes get in sci-fi or some hypothesis about quantum stuff, that any event where more than one outcome is possible creates a different branching universe for each of the outcomes, and if you could somehow travel to one of those places, you’d find someone that was you up to the point of that event, but now has been shaped by different experiences since.