My suggestion is the "War with the Neanderthals".
We could just call it the 1400-Years War, and admit it's just a continuation of the one that quiet down after Lepanto and the last Siege of Vienna.
Or, if we really get serious and decide to end it once and for all, we could call it the Last Crusade. (Though as an Orthodox Christian, given how the Fourth turned out, I'm not sure I'd be thrilled with that option.)