Wendy McKay, aged 54, was found dead in a house in Waltheof Road, Manor, at 1.20am on Sunday, September 24.
An investigation into the circumstances surrounding the death is underway, with one man, aged 36, arrested on suspicion of murder.
He was questioned on Sunday before being released pending further enquiries.
A South Yorkshire Police spokeswoman said: "Detectives investigating the death of a 54-year-old woman in Sheffield have today named her as Wendy McKay.
"At around 1.20am on Sunday, police were called to an address on Waltheof Road, Sheffield, following the discovery of a woman’s body.
"An investigation remains ongoing to determine the exact cause of Mrs McKay’s death.
"Specialist officers are working to support her family and they have asked their privacy is respected at this incredibly difficult time.
"A 36-year-old man was arrested on suspicion of murder in connection with the death and has now been released under investigation."
Anyone with information should call South Yorkshire Police on 101 or Crimestoppers on 0800 555111.