I figure Captain Beefheart sounds like some berk diminutive for a god's name, like "Jizzy Chrizzy". What the local drunk-Catholic-equivalents would call him.
And Beefheart, in said context, makes me think of one of the villains in Ivanhoe--Front-De-Boeuf-which means either "Beef Head" or "Bull's Head", depending on how you look at it.
("Couer-De-Bouef"--heart-of-beef--is a kind of tomato, also known as a "custard apple" so that's a bit of a dead-end, metaphysically speaking.)
"Bull's head" works perfectly, of course.
Thinking about Bull Gods, and William Gaddis, I remember Mithras--"I shall sacrifice to his mace, well aimed against the skulls of the Daevas". Well if he's not a god just waiting to play D&D, then who is?
In addition to cattle, Mithras is a god of the harvest (who isn't?), and contracts.
So I figure: Minotaur god, cult expanded northward from the middle-east, Clerics having mysterious powers and taboos concerning covenants and oaths, spells concerning truth, lie detection, et al. My work here is done.