Gov. Cuomo has vetoed a bill that would have let state lottery winners remain anonymous.

Cuomo explained that publicizing the winners’ names keeps the lottery commission honest.

“Being able to publicly present a grand prize winner . . . provides accountability to members of the public who have also been playing the game,” he said.

Publicizing the name also “provides comfort that there was an actual winner’’ and ensures that the state is not “adding all the money to its own coffers,’’ he said.

Cuomo noted there’s long been a way to get around the anti-privacy rules: a winner can still create a limited liability corporation, or LLC, to collect the prize in its name.

The bill Cuomo vetoed had been popular, passing in the state Senate, 61-1, and in the Assembly, 140-3.