1705 as abbreviation of reputation (n.); upon rep "I swear it" was a common 18c. slang asseveration. As a shortening of repetition (n.) it is recorded from 1864, originally school slang; as a shortening of representative (n.), especially (but not originally) "sales representative," it is attested from 1896. As an abbreviation of repertory (company) it is recorded from 1925.
type of corded fabric, by 1860, from French reps, which is of unknown origin.