Confused, he searched his name on Facebook and found dozens of impostors. The accounts used photos of him at the gym, at his brother’s wedding and at war. He reported the fakes to Facebook, which said in automated responses that many didn’t violate its rules. When the company did remove some of the knockoffs, more popped up in their place.

I met Anonsen while reporting Sunday’s special hourlong episode of “The Weekly,” a new television show from The Times, about online scammers using military identities to steal money from unsuspecting civilians on social media. While there are no figures for how many service members have been affected, the F.B.I. said it received nearly 18,500 complaints from victims of romance or similar internet scams last year, with reported losses exceeding $362 million, up 71 percent from 2017.

When Facebook did little to stop the spread of fake accounts using Anonsen’s information and photos, he went to his platoon commanders and later his battalion’s intelligence officers. “I let them work their military-intelligence magic, and I went back to them, and they’re like: ‘We can’t do anything about it, man. It’s out of our hands,’” he recalled. “I thought military intelligence would be able to type a couple of zeros and ones and it would all go away, but it’s not that simple.”

Anonsen, 31, separated from the Marine Corps last year, and though he abandoned Facebook and Instagram in 2017, his impostors have remained on the sites. He worries this digital reputation could affect his career prospects. He got a job as a commercial diver aboard a ship in the Gulf of Mexico, but he’s still looking over his shoulder.