Sabita Thanwani, a British national and student at City, University of London, lived at Arbour House, Sebastian Street, in Clerkenwell, police said.
She died of serious neck injuries after being attacked at the student accommodation.
Police were called Arbour House at 5.10am on Saturday but Ms Thanwani was pronounced dead at the scene.
Officers have appealed for help to find Maher Maaroufe, 22, who they believe had been in a relationship with Ms Thanwani.
Mr Maaroufe is a Tunisian national who has no fixed address. He is not a student.
Police said Mr Maaroufe is known to travel and has links across London and also travels to Cambridgeshire.
Officers said anyone who sees Mr Maaroufe should not approach him but should call 999 immediately.
Police said Ms Thanwani’s family have been informed and will be supported by specialist officers.
A special post-mortem examination will be arranged in due course.
Detective Chief Inspector Linda Bradley said: “I am reiterating our urgent appeal for information to trace 22-year-old Maher Maaroufe. He has links across London, particularly in the Marble Arch, Edgware Road, and Lewisham areas. He is also known to travel to Cambridgeshire.
“One of the images we released shows Maaroufe with dark hair and a moustache and beard. He has now shaved his head, and has little facial hair.
“Maaroufe had been in a relationship with Sabita but he was not a student. He is a Tunisian national of no fixed address.
“Officers are making enquiries to trace those who had contact with him, but I would ask anyone who knew him who has yet to speak with police to please get in touch. I would again ask the public not to approach him if they see him, but call 999.
“I am also appealing, once again, for Maher Maaroufe to attend a police station immediately. Maher – I am making this appeal directly to you: if you see this, please go to the nearest police station. It is important that we speak with you.”