Avon and Somerset Constabulary has confirmed that the woman who died on Sunday in the incident at a property in Morley Street, Barton Hill was Amal Abdi, aged 21.
Amal, who is Somalian, was four months pregnant and the post mortem has confirmed that she died from stab wounds.
The family have released a photo of Amal.
A 21-year-old man who was arrested on suspicion of her murder remains in police custody. A further warrant of detention has been obtained, enabling officers to continue questioning him.