Lucy Clews, aged 39, was pronounced dead at a property on Bath Road in West Chadsmoor on December 29 shortly after 12.40am after concerns were raised for her welfare.
A post-mortem examination found Ms Clews had been repeatedly stabbed, a Staffordshire Police spokesman confirmed.
A 26-year-old man, of no fixed abode, was arrested on suspicion of murder on December 30. He has since been released under investigation whilst further enquiries continue, but he remains in custody due to an unrelated matter.
Detectives said there will continue to be a police presence – and a cordon – at the property whilst further forensic investigations are carried out. It is likely to remain in place for the rest of the week whilst increased neighbourhood patrols, to provide reassurance assist with evidence gathering, take place.
The investigation is being spearheaded by the force's major investigation department and the senior investigating officer, Detective Inspector Cheryl Hannan, is asking anyone with information to come forward.
She said: "We are keen to establish Lucy’s movements over the Christmas period and the circumstances leading up to her death. I would ask any members of the public living in the area to check any smart doorbell or CCTV cameras they have for anything that looks out of place or captures Lucy’s movements.
"Plus, if you have any information about this incident, no matter how small or insignificant, please help us by getting in touch using any of the options below."
On New Year's Eve Lucy's family paid tribute to her, saying: "We are suffering the terrible sudden loss of a very special granddaughter, daughter and sister.
"Lucy will never be replaced in our hearts and will forever live in our memories."
People can contact the force via the Major Incident Public Portal website. Alternatively, for guaranteed anonymity, contact Crimestoppers online or on 0800 555 111.