Jobari Gooden, 27, was stabbed after a broad daylight fight near the House of Ramish 2 barber shop on Choumert Road at 3.15pm on Friday.
Medical staff battled to save his life but he was pronounced dead at around 6pm.
His next of kin have been informed and are being supported by the police.
A post-mortem examination will be held in due course.
Detective Brian Howie, the senior investigating officer, said: “We need to hear from anyone who was in the area and saw what happened as a matter of urgency.
“This attack took place in the early afternoon and in the middle of Peckham Rye. We know the area was busy, with people going to the shops or the market.
“I expect that many people saw the fight, the knife that was used, and subsequent fatal attack. Did you see where the suspect went?
“We’re a week away from Christmas, and at a time when many families come together to celebrate, another family is grieving following a violent attack in the heart of the community. I would ask you to do the right thing and call the police.
“If you do not wish to speak with us, you can contact Crimestoppers in confidence. Any bit of information could be vital.”
No arrests have been made.
A crime scene remains in place, and several roads in the vicinity including Rye Lane, Choumert Road and Bournemouth Road are closed to traffic.
Detective Chief Inspector Daniel Smith added: “Our thoughts are with Jobari’s family as they come to terms with this loss.
“To have a loved one taken from them in these circumstances just days before Christmas is devastating.
“We understand that the community will be shocked at the brazenness of such an attack, taking place as it did in the afternoon on a busy shopping street.
“We share that shock and would like to reassure residents that officers will be in the area in the coming days, providing a visible policing presence and ensuring local people can go about their business safely and without fear of violence.
“I’d urge anyone who has concerns to speak to officers. They are there to help and to provide reassurance in whatever way they can.”
Anyone with information is asked to call police via 101 quoting reference CAD 4252/17Dec. To remain anonymous, call Crimestoppers on 0800 555 111.