Murder detectives are continuing to question a prisoner arrested on suspicion of killing a fellow inmate at Coldingley Prison near Woking.
Madala Washington, 25, died after being attacked at the prison in Bisley at around 1pm on Friday.
Surrey Police said he had been the victim of a "serious assault" at the prison, which houses around 500 inmates, and detectives have launched a murder investigation.
A 23-year-old man, who is also an inmate at the prison, was arrested on suspicion of murder and remains in police custody.
A spokesman said: "A 25-year-old man, believed to be from south-west London, was sadly declared dead at the scene.
"Officers from the Surrey and Sussex Major Crime Team are making a number of enquiries to establish the circumstances surrounding the incident and are working with HM Prison Service and the Ministry of Justice."
The Prison Service said an investigation would be carried out by the independent Prisons and Probation Ombudsman.
Coldingley is a category C training prison, meaning inmates are considered unlikely to make a determined escape attempt but cannot be trusted in open conditions.
It has capacity for around 500 prisoners in five wings, where inmates are mainly housed in single cells, and is focused on the "resettlement of prisoners".
The death comes against a backdrop of concerns about rising cases of violence in UK prisons.
There were 257 deaths in custody last year including eight homicides, more than in any other year since records started in 1978.
In 2015 Coldingley's independent monitoring board wrote to prisons minister Andrew Selous over its concerns about the jail.
Its report blamed an increase in home-made weapons at the prison and illegal drugs on cuts to the number of prison officers and staff.
Steve Gillan, general secretary of the Prison Officers Association, said: "We do not comment on ongoing police investigations, but generally there has been an increase in violence, and indeed homicides, in our prisons.
"We believe that is due to the lack of prison officers - some 7,000 have been made redundant since 2010.
"Our prisons are a more violent place than they have been. It is tragic that someone has lost their life."