That’s getting into ship of Theseus territory which is similar, but slightly different than the transporter paradox. It gets closer when you do the whole build another ship out of the replaced parts thing, but with the transporter there’s something that gets destroyed and that something is where your consciousness is.

Even a “perfect” copy is still a copy, and the fact that the second consciousness doesn’t rely on the first to exist (they could simultaneously exist ala William Riker) it’s a separate instance so a separate person.