Madala Washington, 25, from south-west London, died at the prison in Bisley after being assaulted at about 13:00 BST on Friday.
Surrey Police said it was continuing a "thorough and extensive investigation" to establish the circumstances surrounding the death.
A 23-year-old inmate who was being held by police has been bailed until 2 June.
A man arrested on suspicion of murder after the death of an inmate at HMP Coldingley has been bailed.