Can one say “have you nominated” or would you require an object, “have you nominated yourself”?
Context is that of an election, for example.
According to the Oxford English Dictionary, nominate is usually transitive and thus requires an object (“I nominated someone”). However, there are a few exceptions in which the verb is intransitive:
intr. Austral. Polit. To put oneself forward formally as a candidate for election; to register one’s candidacy. Usu. with for.
Snooker and Pool. To specify (a ball) as the object ball to be hit next by the cue ball; (also in Pool) to indicate (the set of balls) as the set one will aim to pot; to specify (a pocket) into which one is aiming the next ball. Also intr.
trans. To choose (a mare) as suitable for mating to a particular stallion. Also intr. with to.
Thus, in the context of an election it can usually be expected to require an object. However, there are a few cases in which this is not true.