Brahane Yordanos, originally from Eritrea, was killed at her home in the Lozells area of Birmingham on Saturday morning.
Police named her as the victim on Sunday as they appealed for anyone who knew her to get in touch so her relatives can be informed of her death.
Meanwhile officers are continuing to search for a man who was seen leaving the area shortly before emergency services were called to the house of multiple occupancy in Unett Street where Ms Yordanos was killed.
Police initially thought the suspect was a man known to the victim but he has since been ruled out of the investigation.
Detectives are trawling CCTV and appealing for anyone who visited Ms Yordanos overnight on Friday to come forward.
Detective Inspector Jim Mahon, from the West Midlands Police homicide unit, said: “Our investigation is progressing at pace, but we are struggling to find anyone who knew much about her.
“We desperately need to speak to her family to inform them of her sad death. This may also give us leads to who she may have been associating with.”
The building remained cordoned off on Sunday as officers examined the scene.
Anyone with information is asked to contact police quoting log number 765 of July 31, or to contact Crimestoppers anonymously on 0800 555 111.