RALEIGH, N.C. — If you are lucky enough to win the lottery here, there is one thing you are virtually certain to lose: your privacy.

Like most of the 44 states with lotteries, North Carolina considers the identities of winners of large prizes to be a matter of public record. But this year, in which winners already have come forward more than 40 times to claim awards that the state later publicized, lawmakers have considered whether the winners should be allowed to collect their money without having their names disclosed.

At the urging of lottery officials who warned that anonymity would threaten the appeal of the games — and ultimately the revenue that flows into the state’s treasury — a legislative committee rejected the proposal last week. The issue, though, has surfaced in at least 10 states in recent years, and industry executives believe it will continue to be a subject of debate at a time when dozens of state governments rely on lotteries to relieve their strained budgets.

“I think it’s the curse of the lottery that your name is out there forever,” said Patrick Nowlin, who lives in southern Wisconsin and won a $41 million Powerball jackpot in 2007. “You’ve always got to keep looking out for a scam. Even after seven years, every once in a while I get a suspicious phone call.”