Billy Henham, 24, from Henfield, West Sussex, was found dead inside a building in North Street on Thursday afternoon.
His body was discovered at the city centre property after police were called to reports of concern for a person.
A sixteen-year-old boy, of no fixed address, and an 18-year-old man, from Greenwich, London, were initially arrested on suspicion of murder.
A third suspect, a 26-year-old man from Hove, was later arrested. All three remain in custody.
Sussex Police are appealing for anyone who saw Mr Henham in Brighton from 6pm onwards on 31 December, New Year’s Eve, to get in touch.
Detective Chief Inspector Mark Chapman, from the Surrey and Sussex Major Crime Team, said: “Our thoughts are with Billy’s family and friends at this difficult time.
“We are continuing to conduct enquiries in the city centre to establish the circumstances and are appealing for any witnesses to come forward.
“We would particularly like to hear from anyone who saw Billy on New Year’s Eve in Brighton from about 6pm onwards.”
Brighton and Hove Superintendent Julia Pope added: “We have officers on patrol in the city and at the scene and anyone with concerns or any information can speak to them.”
Anyone who can help the investigation is asked to report it online or call 101 quoting Operation Gatlin.
To give information anonymously, contact Crimestoppers on 0800 555 111.