Voting across the United States is registered, and voter registration requires identification. In Cook County, where I vote and election judge, voters are assigned to relatively small precincts, which track votes during the day on paper and electronic ledgers. If Judy Blue comes in and votes in the morning and you try to come in and vote for her later, you won't be able to check in. If the reverse happens, Judy makes a stink and there's a process for going through the ledger and checking identification. In practice, neither thing ever actually happens: "retail" voter fraud in the United States is practically nonexistent. It's an expensive crime with stiff penalties that is extraordinarily unlikely to impact the election.
The people who object to voter ID laws don't also object to voter registration ID laws? I thought they were worried about people who never had ID, but how would they register?