Moaning Minnie

All the evidence points to British slang for an air raid siren and then army slang for the German Nebelwerfer Mortar, both from WWII. (It was never, as is often wrongly supposed, a WWI expression for the German minenwerfer or trench mortar.) After WWII, the expression acquired its current meaning of a habitual grumbler or complainer, chiefly because of the alliteration.