Who is Sammy Jenkins?

Sammy Jenkins is a pivotal character in the movie, allowing for exposition and insight for Leonard's illness and character. But who is he really?
It is my belief that Sammy Jenkins is Leonard. After all, the movie has so many different possibilities. Leonard could be faking his own illness, Teddy could be lying, and Natalie could have even stolen the money.
Several times throughout the film, Nolan decides to interchange Leonard's character with Sammy. One instance was during a flashback where Sammy was in a hospital; Leonard was soon imprinted over him. This happens again at the end, in which Teddy tries to tell the truth, and Leonard replaces Sammy in a flashback. This leads me to believe that Leonard's brain safeguarded him by creating a new identity. He couldn't deal with the fact that he killed his wife, so why not put the blame on someone else?
Teddy also repeatedly states throughout the film that Leonard is not really Leonard. It's who he "used" to be. This suggests that Leonard has gone through several identity changes. Perhaps each time he remembers what he did to his wife, he repeatedly makes a new persona. This is also further proved by Leonard stealing John G's clothes. Leonard states, "I'd rather be mistaken for a dead man than a killer."
If Leonard wasn't Sammy Jenkins, then what is the point of his inclusion? The only thing I can think of would be to remember his illness, yet Leonard remembers the incident, which is what gave him his illness in the first place.