Surely just because there are two identical bodies, these bodies cannot be the same person. They would live two different lives. Therefore, the body theory alone cannot be considered a necessary and sufficient definition when defining personal identity. Another common theory of personal identity is the soul theory. The problem with this theory is arrived from the definition of a soul.
Soul is a very difficult term.
However, since no one has ever seen, felt, touched, smelled, or tasted a soul, it is a mysterious phenomenon. Since we have no clear and distinct idea of a soul , it would not be wise to base the definition upon it. For instance, some religions believe in reincarnation after death. This is when a soul enters another body. With this in mind, someone's soul such as Elvis could become reincarnated in someone else named John.