Alas, for me "Big Bad Wolf" reminds me of "Bad Wolf" from Dr. Who. But I think you'd only find that correlation coming from Whovians and I doubt any would raise objections.
My first inclination (forgive me) is to go for comic relief with something silly like "snickers" (apologies, apologies, apologies, I haven't had coffee yet this morning.)
If it ties in with your Red story why not "Red Wolf?" with Red for short? then you could have a line later that goes "red for dead." (a play on anti-communist "better red than dead" from long ago history)
Sigh, I'm useless.