Imagine being told that you were born with a different name, that you had family members you had never met, that your entire life was being orchestrated by a total stranger. That's exactly what happens to Adam Farmer as a teenager. Talk about an identity crisis! What we learn from Adam is that identity is more than a name and a persona: it's a history. Without a history, without your past, you can't really know who you are. Adam's personal history is missing not only because his family was placed in the Witness Re-Establishment Program, but also because his memory is shot. He can only remember bits and pieces of his past, and from the looks of it, he's stuck reliving the same events over and over, without realizing it. It's like the worst Groundhog Day ever.
Name, shmame. It doesn't matter that Adam changed his name and moved away from his hometown, he's still the exact same person he was before.
People with amnesia can't have an identity, because in order to know who you are, you have to know who you were.