[There appear to be a serious number of beefheart fans on b3ta, it would seem.]
DrZaarlon Wholly Approves Of This Picture!
(DrZaarlon Is Ranked #1 On Google For Horse Porn., Sun 16 Dec 2007, 13:50, archived)

Captain Bee Fart
seems to be a popular version.
( mofaha : howling down the chimney, Sun 16 Dec 2007, 13:52, archived)

According to music folklore, so this might be complete bollocks,
He came up with the name whilst holding his little friend in his hand on acid, and exclaimed to Frank Zappa 'it's a Beefheart!'
( Jahled The most heroic gerbil in Guildford, Sun 16 Dec 2007, 13:54, archived)