The woman was found at a home on Bath Road in West Chadsmoor, Cannock, at 12.40am on Wednesday after police received calls concerning the woman's welfare.
Staffordshire Police have now said the victim, who was pronounced dead at the scene by paramedics, was identified on Friday as 39-year-old Lucy Clews.
Detectives have now launched an appeal for information after a post-mortem examination found her cause of death to be multiple stab wounds.
Lucy's family paid tribute to her in a statement, 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.
"We ask for our privacy to be respected as we come to terms with what has happened."
A 26-year-old man, of no fixed abode, has been arrested on suspicion of murder and remains in police custody.
Detective Inspector Cheryl Hannan, of Staffordshire Police’s Major Investigation Department, said: "If you have any information about Lucy’s movements over the Christmas period, please get in touch.
"Did you see her in the Cannock area or hear from her?"
Anyone with information is asked to contact Staffordshire Police or contact Crimestoppers anonymously on 0800 555 111.