The story
From goat + fish. The Mullidae sense is because of the fish's beard (as it were) seeming like a goat's beard (a goatee). The chimera sense is because the mythical beast is half goat and half fish.
Etymology from Wiktionary, CC BY-SA 4.0.
goatfish
Today it means: Any of the family Mullidae of brightly coloured fish with two barbels on the chin. Full definition →