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."

Passwords were found on public websites such as Pastebin, where hackers often dump data.
Recorded Future said it was impossible to say whether all the passwords were active.
The details were likely to have been stolen when used to access malware-ridden sites.
Recorded Future's report said many government employees had used their official emails, and possibly the same passwords, to log in to third-party web services that had been hacked.
The company scanned more than 680,000 web sources over the course of a year. It found 705 emails and passwords originating from government agencies.
The data was connected with the departments of defence, justice, the treasury and energy as well as the CIA and the director of National Intelligence.
"The presence of these credentials on the open web leaves these agencies vulnerable to espionage, socially engineered attacks, and tailored spear-phishing attacks against their workforce," the company said on its blog.
Recorded Future called on government departments to make their networks more secure by requiring staff to use two-factor authentication, which requires users to have two separate components to their log-ins, and only allowing them to remotely access their systems via virtual private networks.
"It isn't that these agencies don't know what to do, it is just that they aren't implementing the changes," said Scott Donnelly, a senior analyst at Recorded Future.
A man who died during a shooting at a pool party in Surrey has been named as 34-year-old Ricardo Hunter.
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A security intelligence company has found the stolen log-in credentials for up to 47 US government agencies accessible online.