Esther Brown was found at her West Princes Street home in Woodlands, Glasgow, at about 4pm on Tuesday but she had not been seen since Friday at about 5.30pm.
Police confirmed the identity of the 67-year-old on Thursday as a postmortem examination was carried out to determine her cause of death.
Officers are hunting “whoever is responsible for this woman’s death” and have appealed for witnesses.
Superintendent Ross Allan said: “I would like to begin by offering on behalf of Police Scotland our deepest condolences to the family of Esther Brown at this deeply distressing time.
“Esther was a much loved and active member of the community here in the Woodlands area of Glasgow through her charity work and her willingness and commitment towards helping others.
“I know and understand the terrible impact that this suspicious death has had on the wider Woodlands community and local residents have seen, and they will continue to see, an increased number of police officers in addition to the incident caravan we have parked nearby.”
Senior investigating officer, Detective Superintendent Suzie Chow, said: “I would like to again appeal for anyone that can provide information to do so – people who own commercial premises or dashcam and CCTV, if you could come forward please make yourself known to the police so we can secure that footage.
“We know (Ms Brown) was last seen on Friday evening about 5.30pm in this area so again I would like to appeal to anybody who may be able to help us piece together her movements and establishment exactly what’s happened.
“We’re about 36 hours into the investigation and as you’ll understand we’re dealing with a suspicious death so we have to cover all angles and all aspects to try and piece together the movements.
“I’d like to thank the public for their information coming forward and helping us with our inquiries, it’s been really positive and a lot of people have a provided information.”