1868, "appointed or nominated but not yet installed," past-participle adjective from designate (v.). The baseball designated hitter "substitute named before the start of a game to hit for the pitcher" was introduced in the American League in 1973; it soon gave wide figurative extension to designated, as in designated driver (by 1985).
early 15c., "marked out, indicated" (a sense now obsolete), from Latin designatus, past participle of designare "mark out, devise, choose, designate, appoint," from de "out" (see de-) + signare "to mark," from signum "identifying mark, sign" (see sign (n.)). Meaning "appointed or nominated but not yet installed" is from 1640s.
1580s, "a request, demand, petition," from Latin postulātum "demand, request," properly "that which is requested," noun use of neuter past participle of postulare "to ask, demand; claim; require" (see postulate (v.)).
The sense in logic, "proposition proposed for acceptance without proof, something taken for granted," is from 1640s, from a sense in Medieval Latin. The meaning "self-evident practical proposition" is by 1751. The earlier noun in English was postulation "a petition, request" (c. 1400). Middle English also had postulate (adj.) "nominated to a bishopric or archbishopric" (mid-15c.).
1540s, "to call or mention by name" (common in 17c., but now rare or obsolete), a back-formation from nomination or else from Latin nominatus, past participle of nominare "to name, call by name, give a name to," also "name for office," from nomen "name" (from PIE root *no-men- "name"). Later "to appoint or designate by name to some office or duty" (1560s); "to propose or formally enter (someone's name) as a candidate for election" (c. 1600). It also occasionally was used from c. 1600 with a sense "give a name to." Related: Nominated; nominating.