Shara Miller, aged 41, was found off Woodburn Road just after 6.10am.
West Midlands Police said nothing could be done to save her and she was confirmed dead at the scene.
Following enquiries, three men, aged 29, 38 and 31 have been arrested on suspicion of murder.
They remain in custody for questioning.
Officers believe Shara was killed in the early hours of the morning at the location where her body was discovered.
They are asking the public for any information surrounding her movements before 1am.
Detective Chief Inspector Alastair Orencas from our 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.”