Police were called shortly after 6pm on Tuesday to reports of people fighting on North Walk.
Officers attended along with the London Ambulance Service and two men were found nearby with stab wounds.
Bradley Hutchins, aged 20, was pronounced dead at the scene.
His family are being supported by specialist officers.
A post-mortem examination gave the cause of death as a stab wound.
The second man, aged 19, was taken to hospital for treatment.
His injuries are not believed to be life-threatening.
A 20-year-old man was arrested on suspicion of murder and has been bailed to return on a date in mid-October.
Detective Inspector Jason Fitzpatrick, leading the investigation, said: “We have spoken to several people as part of our enquiries, however we believe there may be others who witnessed the incident or the moments leading up to it and would ask them to come forward.
“We are continuing to review CCTV and would also ask anyone who has a video doorbell, or who was driving in the area with a dash cam, to please check their footage.
“It is vital that we establish what happened and locate those responsible.”
Superintendent Mitch Carr, from the South Area BCU, said: “First and foremost our thoughts are with Bradley’s family and friends who have suffered an unimaginable loss.
“We know that there will also be significant concerns within the wider community in New Addington and you will see additional officers in the area, while we continue to investigate this tragic crime.
“I would ask that you speak with them if you have any information. It is only by working together that we can reduce violent crime, and we need your help with this investigation.”
Any witnesses are asked to call 101 or post @MetCC quoting reference CAD 6879/12Sep. To remain 100% anonymous contact the independent charity Crimestoppers on 0800 555 111.