Sarbjit Kaur's body was discovered by her family members at their home in the town of Wolverhampton last Friday.
West Midlands Police said they are keeping an open mind on the motive of the 38-year-old's murder as it released the victims name on Monday as part of a public appeal for information.
Kaur was attacked inside her own home. This is a shocking case, the likes of which are extremely rare, and we have a team of officers working on this murder inquiry to establish what happened and to finding the person or people responsible, said Detective Chief Inspector Chris Mallett, who is leading the West Midlands Police Homicide Teams murder investigation.
He confirmed that early inquiries have revealed that some items were taken from the home but added that the motive so far remains unclear as his team continues to investigate several lines of inquiry, including whether this was a random burglary or if the address or Kaur were deliberately targeted.
The interior was in an untidy state - which could indicate it had been searched - and we believe that some items are missing. We are working with the family to understand exactly what items were taken, Mallett added.
Police have carried out CCTV and house-to-house inquiries as well as conducted an extensive forensic examination of the scene as they try and piece together Kaur's movements throughout the day.
Kaur was assaulted during the attack and pronounced dead at the scene. A post-mortem has proved inconclusive on the precise cause of her death, with further tests being carried out by pathologists.