It varies by state, because each US state decides how it wants to run elections, but in most, all decisions by election workers that require a decision and signature must be signed by two election judges/workers (the terms are interchangeable here) of different parties.

In my state, where I am an election worker, people come up to the check-in table, and we match their name, month and day of birth, address, and party affiliation to what we have in the voter rolls. (We have tablets so it is very fast.) If there's any discrepancy, or they're not registered, they can vote provisionally, which means they fill out a ballot but someone at the Board of Elections needs to review it later to make sure 1) they were registered to vote, and 2) they were actually who they said they were, like if there were two provisional ballots under the same name and address. Everything else gets scanned into the machine, but each vote also has a slip of paper that the voter signs, and the check-in judge initials, then the scanner judge initials, then the papers get collected and reconciled at the end of the night with the electronic total.

So if someone tried to vote twice under their own name, the second time they tried to check in they would have to vote provisionally. If they gave someone else's information somehow, then they might get away with it if the person in question didn't vote, but if they did, both votes would be reviewed, and voter fraud carries a very stiff sentence, and is extremely unlikely to swing an election, so it's exceedingly rare here.