He was Ewan Richard Maxwell, 55, of Queenstown.
Mr Maxwell died about midday on Friday when he lost his footing on a steep cliff and fell about 100 metres. He was dead by the time his hunting companion reached him.
With no cellphone coverage, his friend had to trek through rugged terrain for about eight hours and was "obviously cut up" and not in a condition to talk to media, Constable William Parker said.
Both men were experienced hunters and had been in the popular hunting area since Tuesday.
Mr Maxwell's body was recovered yesterday.