LEBANON, Tenn. — Growing up in a small Tennessee town, Lane Martin looked every day at the photo of his uncle hanging in the kitchen but knew only a few things about him: He had left Harvard Law School at the start of World War II to join the Marine Corps; he was killed in 1943 storming a Pacific atoll called Tarawa; and his body came home in a gray steel coffin after the war and was buried in a clover-covered family plot.

But in 2020, Mr. Martin got a phone call from the Marine Corps. There had been a mistake, he was told: His uncle — Capt. Edward Glen Walker Jr. — wasn’t in that gray steel coffin after all. Instead, he had been found in an anonymous grave in a military cemetery in Hawaii.

The woman on the phone said the military planned to return Captain Walker’s remains and try to figure out who had been buried all those years in the captain’s grave.

“I honestly thought it was a hoax,” said Mr. Martin, who was born nine years after his uncle died and is now retired. “But they started describing the evidence, and a shiver went down my spine, and I said, ‘My God, they’ve got my uncle.’”

Improved forensic techniques and DNA testing can now reliably identify war dead that the military once thought would remain forever anonymous. But the advance comes with a twist: The same technology that can name the nameless can also reveal mix-ups and blunders that caused service members to be buried in the wrong graves.

After World War II, the U.S. military had to sort out the remains of nearly 300,000 war dead. Most were sent home to families or buried overseas in marked graves. But about 8,500 sets of remains could not be identified at the time. These were buried in American military cemeteries under precise rows of marble markers bearing only the word…