register has 7 distinct synonyms spread across 6 of its 17 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
enroll to vote
“register for an election”
have one's name listed as a candidate for several parties
show in one's face
“Her surprise did not register”
send by registered mail
“I'd like to register this letter”
enter into someone's consciousness
“Did this event register in your parents' minds?”
an official written record of names or events or transactions
(music) the timbre that is characteristic of a certain range and manner of production of the human voice or of different pipe organ stops or of different musical instruments
a book in which names and transactions are listed
(computer science) memory device that is the part of computer memory that has a specific address and that is used to hold information of a specific kind
an air passage (usually in the floor or a wall of a room) for admitting or excluding heated air from the room
a regulator (as a sliding plate) for regulating the flow of air into a furnace or other heating device
a cashbox with an adding machine to register transactions; used in shops to add up the bill
Synonyms, antonyms and the broader and narrower relations for register come from Princeton University’s WordNet. Full sources and licences.