Pima County Sheriff's officials announced Wednesday that the victim was 55-year-old Dorease L. Clarke.
Authorities believe she was the live-in girlfriend of 56-year-old Myron Elliot Fletcher.
Fletcher is being held on a $100,000 bond in the county jail on suspicion of first-degree murder.
Investigators found the woman's remains March 18 in the master bedroom of a home after sheriff's deputies conducted a welfare check.
She couldn't be positively identified because of the condition of the body.
An autopsy report released last Friday shows the victim was shot multiple times.