The commission oversees hundreds of millions of dollars in revenues and prizes a year.

“When somebody wins a public lottery of $560 million, there is a public interest in knowing who the winner was, and that it is a fair and equitable process,” John J. Conforti, an assistant attorney general representing the lottery commission, told the court.

The state gave little credence to the argument that identifying Ms. Doe would jeopardize her safety, saying that any risk could be managed by engaging a security detail. Ms. Doe’s lawyers said they were already lining up bodyguards.

Most states view the names of winners of significant prizes as a matter of public record, though a few permit winners to keep their identities private. Some states, including New Hampshire, allow trusts and not just individuals to claim winnings.

For almost two hours Tuesday, Judge Charles Temple of the Hillsborough County Superior Court heard arguments in the case, which has made headlines around the world for the eye-popping size of the prize and for an “if only” twist in Ms. Doe’s plight.

When Ms. Doe realized she had the winning ticket, she followed the instructions on the ticket and on the lottery commission’s website to “sign the ticket.”

If only she had talked to a lawyer first, she might have avoided the entire issue. She could have set up a trust that would sign the ticket, claim the prize and be the public face of the winner, rather than Ms. Doe personally. But lottery officials say the chance to do that ended when she signed her name.

Ms. Doe’s lawyers — Steven M. Gordon and Billy Shaheen, high-powered attorneys in the state — said the ticket and state’s website were misleading because they did not explain that by signing a ticket, winners give up their anonymity. Nowhere, they said, does the website advise the winner “that there is an option for a trust to claim a prize.”