The story
Possibly from the French name Minié (for a soft lead bullet) or the German Minenwerfer, a type of trench mortar (WW I allusions), or simply because of the alliteration of the name with the participial adjective; see Martin, Gary (28 November 2022), “Moaning Minnie”, in Phrases.org.UK, retrieved 29 Nov 2022.
Etymology from Wiktionary, CC BY-SA 4.0.