Rina Yasutake, aged 49, lived in Bondgate, the street where her remains were found on Tuesday evening after the police were alerted by a member of the public.
They have appealed for anyone who knew her to come forward.
Two women, aged 51 and 75, and a 46-year-old man have been arrested in connection with the discovery of Ms Yasutake's body.
All three have been released on police bail while the investigation continues.
Ms Yasutake's death is being treated as unexplained by detectives.
Tests are under way to establish how and when she died, but officers want to establish a timeline of her movements before she died and want to speak to anyone who knew her.
Senior Investigating Officer, Detective Chief Inspector Nichola Holden, said: “We realise this incident has caused concern among the local community in Helmsley and we thank everyone for their understanding while we carry out what is a very sensitive investigation into Rina’s death.
“To assist with our investigation, I am appealing to local people and anyone in the wider area who knew Rina, not just as a friend, but also by sight, to please contact us, no matter when you last saw her. Your information could be vital in helping us establish the timeline prior to her death.”
Anyone who knew Ms Yasutake, or knew of her, can contact North Yorkshire Police on 101 and pass information to the Force Control Room, quoting incident number 12180179672.
Information can also be passed anonymously to Crimestoppers on 0800 555 111.