Edgar was a man who worked in demolitions but was taken over by a Leviathan.
The real Edgar was fixing his car when he heard rattling coming from the sink. When he went to investigate, black goo shot out and entered his body. Within seconds, he was fully possessed.
The Leviathan that took him would come to be known by his name. Upon being decapitated by Sam Winchester, the real Edgar was unlikely to survive and given how the Alpha Vampire prevented the Leviathan's regeneration by keeping the head separate from the body, this is most likely the case.