Maxine Davison, also known as Maxine Chapman, aged 50, was the mother of the offender Jake Davison.
Further victims were Sophie Martyn, aged three, and her father Lee Martyn, aged 40.
Stephen Washington, aged 59, was also killed.
The final victim was Kate Shepherd, aged 66, who was injured at the scene and died later at Derriford Hospital.
All the deceased lived locally in the Keyham area, police said.
The offender has been named as Jake Davison, 22. Police have confirmed he had a firearms licence and used a pump-action shotgun in the shooting spree, which police said was not terror-related.
Davison shot seven people in total around the Keyham area of the city on Thursday evening in a shooting spree that lasted six minutes, before turning the gun on himself.
Police are continuing to investigate 13 scenes within the cordon in Keyham which is expected to remain in place throughout much of the weekend.
A candlelit vigil will be held in North Down Crescent Park in Keyham at 9pm on Friday to pay tribute to the victims of the tragedy.
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