Well, I will say that a movie is "the same movie", whatever it is stored on analog film, optical support, magnetic support or ssd storage. The content and the physical support are different issue. I'll say that a movie "changed" if you cut or add some scene, or add subtitles, ... but not if you copy the file from your magnetic hard disk to an USB key, even if there are much more differences at physical level between the HD and the USB key.
The same is true for personal identity, in my point of view. The personal identity is in the configuration of neurons, and even in the way changes propagate on the neural network, not in the specific matter distribution. Then, personal identity is not binary (am I the same I was one week ago ? and 20 years ago ?). But to a point yes, you can theoretically have two distinct "persons" with the "same" personal identity, if you can duplicate, or scan, a person.