Hmmm - not sure I'd want to be in a band called that. Just imagine people coming up to you and asking "Hey are you one of those dead monkeys?" and having to say yes.
And the headlines in the music press are bound to be along the lines of "the Monkeys spank!" or if it's a bad gig - "you pay peanuts and what do you get?"
Sounds a bit similar to "Dead Kennedys" as well - Jello Biafra etc..