Police said the body had been in the water for between one and three weeks.
The family and friends of Zoe Louise Parker contacted police after officers investigating the woman's death released pictures of her distinctive teeth and rose tattoo.
A Scotland Yard spokesman said Ms Parker, 24, who also used the name Cathy Dennis, was from the Feltham and Hounslow area of west London.
Her severed torso was recovered after it was spotted by a member of the public near Church Road in Battersea on 17 December.
Police said the body had been in the water for between one and three weeks.
Detectives believe it had been cut in half before being placed in the river.
Police released photographs showing her twisted lateral incisor tooth and tattoo, scrolled with the name Zoe, after they were unable to identify her.
They are still appealing for anyone who knew Ms Parker, or who can provide details of her movements over the last three months, to come forward.
She is thought to have had connections with people in the West End and Charing Cross areas of central London.
Anyone with information is asked to call 020 8284 9765, 020 8853 1212 or Crimestoppers on 0800 555 111.