The name was confirmed by the B.C. Coroners Service Wednesday.
Crews, 32, was a resident of Bremerton, Wash.
Crews drove to the Peace Arch border crossing Tuesday just before 2 p.m. PT and shot Canadian border officer Lori Bowcock who was staffing a kiosk, dealing with people entering Canada by car from Washington.
Bowcock was shot in the neck and airlifted to hospital, where she underwent surgery and is in stable condition. Officials said Wednesday she is expected to make a full recovery.
Crews then shot himself and died at the scene, inside the vehicle he was driving, a white van with Washington licence plates.
Crews is believed to have been a tattoo artist working in a tattoo parlour in Silverdale, Wash., about 20 kilometres west of Seattle.
Crews had moved to Bremerton from Las Vegas, where he also worked as an artist. A former work colleague was stunned to hear what Crews had done.
"He was happy-go-lucky. He loved music and art, always fun," said Shannon Bundy, of the Showroom Tattoo Parlor. "I just talked to him two weeks ago and it sounded like life was going good. I don't have any idea why this would happen."