The story
From the Nanking court dialect (later Postal Romanization) romanization of Mandarin 金門 (Jīnmén), from before the modern palatalization of [k] to [t͡ɕ], parallel with names for the four townships of Kinmen Island: Kincheng, Kinhu, Kinning, and Kinsha.
Etymology from Wiktionary, CC BY-SA 4.0.