Margaret McMurdo, 68, was found dead in the property in Bingham Drive on Monday.
Police said there are no suspicious circumstances surrounding her death.
Mrs McMurdo is believed to have been born and raised in Edinburgh.
A police spokesman asked anyone with information on Mrs McMurdo to come forward. He said: "We are appealing for anyone who might have known Mrs McMurdo or her family to contact 0131-311 3131."