they had an un-named person in the local system at the time he was picked up. John Dow is the name they give to unknown persons. That moniker was already in use so they called him B.K. Doe...standing for Burger King...then he remembered his name might be Benjaman. wikipedia:
"Initially, he was known as BK because he was discovered on the premises of a Burger King. Since then, he has chosen to live under the name Benjaman Kyle and insists that his real first name is Benjaman"

http://www.facebook.com/BenjamanKyle

http://en.wikipedia.org/wiki/Benjaman_Kyle

http://www.npr.org/templates/story/story.php?storyId=129668438

"They were calling me 'BK Doe,' " he says. Burger King Doe. "The only thing I could think of that started with a 'K' was Kyle. So I just picked that as my last name. Benjaman Kyle."