Police officers found Sian Roberts at a property in St Helier's Drive, Salford, at about 18:00 GMT on Sunday.
A post-mortem examination confirmed the 36-year-old died from stab wounds to the chest.
Greater Manchester Police have been given more time to question a 36-year-old man who was arrested on suspicion of murder.
Det Ch Insp Terry Crompton said: "We are eager to find out what Sian had been doing and where she had been on the day of her death.
"This is an extremely difficult time for the family."
A woman was stabbed to death before her body was discovered in Greater Manchester, tests have revealed.