Old English cypera "male salmon," perhaps related to coper "reddish-brown metal" (see copper (n.1)), on resemblance of color. Another theory connects it to kip (n.) "sharp, hooked lower jaw of the male salmon in breeding season," which is from Middle English kippen "to snatch, tug, pull," but OED doubts this.
The modern noun usually is a shortening of kippered herring, from a verb meaning "to cure a fish by cleaning, salting, and spicing it" (early 14c.). The earliest attested uses of the verb are to preparing salmon, hence the verb. The modern noun kipper is recorded from 1773 of salmon, 1863 of herring.