A post-mortem examination found that Mr Hunter, from Coulsdon in south London, died from a single gunshot wound at the private event in Headley, near Epsom.
Two other people were also injured in the shooting shortly after 02:30 BST on Monday.
A 36-year-old woman was shot in the leg and taken to hospital while another man was treated for minor shoulder wounds.
A man from London, 38, who was arrested on suspicion of murder and attempted murder remains in custody.
A woman, 30, arrested on suspicion of assisting an offender has been released on conditional bail until September, police said.
Specialist divers have been searching a village pond for the gun used in the shooting, while forensic teams are continuing a detailed examination of the address in Church Lane.
More than 400 people were at the party at the hired house.
The annual event had been organised by reggae dancehall artist Jason White and his girlfriend Summerlyn Farquharson.
He told BBC Newsbeat they used seven security staff with metal detectors to check all the guests as they arrived.
Det Ch Insp Paul Rymarz, from the Surrey and Sussex Major Crime Team, said: "This was a shocking incident where a man lost his life and we are determined to bring those responsible to justice."
He said police intended to speak to everyone who was at the party, and appealed for anyone not already contacted to come forward.
"This incident has understandably sent shockwaves through the Headley community and we are working with our Safer Neighbourhood Team colleagues to update and reassure residents," he said.
"We do not believe there is any ongoing risk to Headley residents."
A man who died during a shooting at a pool party in Surrey has been named as 34-year-old Ricardo Hunter.