Nightside/WMG

Dead Boy traded away his original name as part of his deal.
His name obviously wasn't always Dead Boy, but that's all anyone ever calls him and no one acknowledges that he was ever called anything else. He may not even remember what his original name was.

Dead Boy made his deal with Lilith.
Dead boy never says who he made his deal with, saying something along the lines of worse than the devil and Lilith was hanging around the Nightside for the past 30 or so years in disguise.Any coincidence that when dead-boy made his deal is around the time John was born (John's ~30 years old).
 * Technically, he never said that he'd made a deal with something worse than the Devil, only that the Devil would've given him a better deal.