Investigators have learned the name of a woman who was burned alive — and beyond recognizability — aboard a Brooklyn train last week.

The police identified the woman as 61-year-old Debrina Kawam of Toms River, N.J. She was the victim of an apparently random attack captured in videos that showed her bracing herself against the doorway of an F train in Coney Island, her body engulfed by flames. Hours later, Sebastian Zapeta-Calil, the 33-year-old man accused of attacking Ms. Kawam, was charged with first-degree murder and arson.

Investigators were using every means possible to identify the woman, Eric Gonzalez, the Brooklyn district attorney, said at a news conference last week. They took her fingerprints and collected DNA evidence. They gathered surveillance footage from the subways, hoping to find a clear image of the woman’s face before the fire.

“It’s a priority for me, for my office, for the Police Department to identify this woman, so we can notify her family of what had happened to her,” Mr. Gonzalez said.

On Dec. 22, around 7:30 a.m., Ms. Kawam was sitting motionless, apparently asleep, when Mr. Zapeta-Calil walked up, took out a lighter and set her on fire, according to prosecutors and the police. He then stepped out of the train and sat on a bench on the subway platform, staring as the smoke and flames overwhelmed Ms. Kawam, the police said.

Then, video of the incident shows a man who appears to be Mr. Zapeta-Calil rising and approaching Ms. Kawam. Instead of trying to douse the blaze, he waves a shirt at her, appearing to fan the flames. At least one police officer can be seen walking by her as people on the platform scream.

The smell of smoke had drifted to the upper level of the station, where officers were on patrol, Jessica Tisch, the police commissioner, said at a news conference later that day. They went downstairs and, with help from an Metropolitan Transportation Authority employee, they extinguished the fire.

The officers did not notice Mr. Zapeta-Calil sitting on the bench as they tended to Ms. Kawam. But their body cameras had captured him, and the clothes he wore: a gray hooded sweatshirt, a wool hat, tan boots and paint-splattered pants.

This is a developing story and will be updated.