A person is defined by his consciousness. The mind is the person. If you step onto a transporter pad and arrive at the other end with your personality, knowledge, experiences and memories intact, then it’s irrelevant whether the transporter simply “teleports” you or destroys your physical body and creates a new one. To-may-to, to-mah-to.
Yes, if (as seems to be the case) your consciousness is merely an electrical pattern, then provided sufficient error correction you would be totally unharmed and the same person.
If you believe your physical shell is inhabited by a non-replicable spirit then I suppose a brain-dead corpse would appear on the other end or worse your body possessed by an opportunistic demon from R'yleh or something worse!