Late 19th century; earliest use found in Francis Day (1829–1889), military surgeon and ichthyologist. So called on account of its appearance which resembles a livery.
Definition of livery fish in US English:
livery fish
noun
Irish English, Northern
The cuckoo wrasse, Labrus mixtus.
Origin
Late 19th century; earliest use found in Francis Day (1829–1889), military surgeon and ichthyologist. So called on account of its appearance which resembles a livery.