She was 48-year-old Barni Ganey Mohamed.
Officers say they are still treating her death “unexplained” and are continuing with their inquiries.
A 22-year-old man who was being questioned by police was released on Saturday on police bail pending further enquiries.
Ms Mohamed was found close to Berkeley House, St Mary’s Street, in the town centre at about 7.30am on Friday.
Emergency services were called to the scene, just a few yards from the Sol Central leisure complex, at 7.30am on Friday.
Police sealed off the front of the flats and forensic teams carried out a search of the area and a second-floor flat.
Eyewitnesses described seeing a body covered with a white sheet on the ground in front of the garages at the base of the three-storey block.
Hassan Jama, of the Somali Forum, said the whole community had been saddened by the death. He said the forum had helped her find accommodation in Berkeley House when she came over to the UK from Sweden in 2002.
He said: “She was a very, very good woman, very well-known in the community and well-liked. We are saddened all this has happened. The community is a family and we will do everything we can to help the police.”
Source: Northantset