A police spokesperson said: “Her loved ones are being supported by specially trained officers and our thoughts are with them at this awful time.”
The force is asking the public for any information surrounding Ms Miller’s movements before 01:00 BST on Monday.
Det Chief Insp Alastair Orencas from the force’s homicide unit said: “We have made some significant progress in our investigation and now have three men in custody.
“However, we still want to hear from anyone who saw Shara or spoke to her in the hours leading up to her death.
“We understand she was involved in sex work around the Soho Road, Birmingham, area and believe she may have been driven to Woodburn Road from that location.
“If you have any footage or information, and haven’t yet come forward, please contact us.”
West Midlands Police is increasing patrols in the area where Ms Miller was found and around Soho Road as reassurance.