Abbie Leigh Downing, 27, was found in a property on Plowmans Way, Wingfield, at 3.45am yesterday morning following reports from paramedics they were treating a woman in her 20s with serious injuries.
Her death is being treated as a murder investigation and a local man, 28, has been arrested and remains in custody.
Detective Chief Inspector Andy Knowles, leading the investigation, said: “I know incidents like this can have a devastating impact on the wider community and we are working round the clock to determine exactly what happened to Abbie.
"We would at this point like to thank Abbie’s family for working with us at what must be a truly devastating time for them. I would encourage the public to avoid speculation into what happened as our enquiries continue.
"If you have any information which could assist our officers, please contact 101 quoting incident number 88 of 25 August.”