Junior doctor John McKenna was found in the changing room at University Hospital Crosshouse in Kilmarnock just before midnight on Monday August 7.
John had graduated from Dundee University in 2010 and was on a specialist training programme for anaesthetists, living in Fauldhouse with his wife Heather.
A Police Scotland spokeswoman said: “Around 11.45pm on Monday it was reported the body of a 29-year-old man was found in a changing room at Crosshouse Hospital.
“Enquiries are ongoing. The death is being treated as unexplained.
“A post-mortem will be carried out in due course to establish the exact circumstances of the death.”
The health board’s HR director Patricia Leiser said: “We are aware of an incident involving a member of staff which took place at University Hospital Crosshouse.
“We are assisting police with their investigations. It wouldn’t be appropriate to comment further while these are ongoing.”
The Royal College of Anaesthetists in Scotland said: “We’re saddened to hear of the passing of a member of our College.
“Our thoughts are with his family, colleagues and friends at this time.”