While that would be totally cool from an 80s pop culture perspective, it’s actually false since Batman: The Killing Joke by Alan Moore and Brian Bolland was published in 1988, and Killing Joke (the rock band) was formed about a decade prior (1978).
When asked about the origin of the band name, Jaz Coleman (Killing Joke’s vocalist and keyboardist) once explained:
“the killing joke is like when people watch something like Monty Python on the television and laugh, when really they’re laughing at themselves. It’s like a soldier in the first world war. He’s in the trench, he knows his life is gone and that within the next ten minutes he’s gonna be dead … and then suddenly he realises that some c*nt back in Westminster’s got him sussed - ‘What am I doing this for? I don’t want to kill anyone, I’m just being controlled’. (Laugh At Your Peril With Killing Joke. Allied Propaganda. May 1979.)
The band itself is still kickin’. Check their Facebook page: www.facebook.com/killingjokeofficial