I can't believe nobody has mentioned author Damon Runyon, some of whose short stories are the basis for the musical Guys and Dolls. (His full name was Alfred Damon Runyon.)
Damon Atkinson is an American drummer, well known in the music community for drumming in bands such as Hey Mercedes and Braid. I don't really care for this name. I like Damien better.
A famous bearer is actor Damon Kyle Wayans (born September 4, 1960), stand-up comedian, writer, and actor. He starred in the television shows "In Living Color" from 1990 to 1992, "My Wife and Kids" from 2001 to 2005, and "The Underground", beginning in 2006. He also starred in many movies, including "The Last Boy Scout", "Major Payne" and "The Great White Hype", "Blankman", and "Beverly Hills Cop".