Police say that Adrian Keise – who is from Lambeth – was stabbed during an altercation involving two groups of men in Lower Marsh in the early hours of Saturday 29 October.
Detective Chief Inspector Brian Howie, from the Met's Specialist Crime Command, said: "Our investigation is moving at pace and we have been carrying out a number of enquiries, including a review of CCTV from the area and a forensic examination of the scene.
"We now believe Adrian was involved in an altercation which started near to the Cubana Restaurant before moving down Lower Marsh.
"I am sure that there were people who witnessed what happened who haven't yet spoken to us about what they saw.
“You may have thought it was insignificant at the time, but it could be vital in helping us to identify those responsible."
Police were called at 2.15am on Saturday to reports of a stabbing outside the Cubana restaurant in Lower Marsh.
Officers attended along with the London Ambulance Service. It was reported that a 32-year-old man had been stabbed.
At around 2.30a, the man was found near to a block of flats in Frazier Street. He was treated at the scene before being taken to hospital. Despite the efforts of emergency services, he died a short time later.
DCI Howie added: "Adrian had the rest of his life ahead of him and my thoughts are with his family and friends as they come to terms with his tragic death. I would urge anyone with information to do the right thing by them and contact us today."
A post-mortem examination will take place in the coming days.
Anyone with information that could help the investigation is asked to call 101 quoting CAD 681/29Oct.
You can also share information, photos and videos directly with the investigation team on the dedicated police web portal.
To remain anonymous contact the independent charity Crimestoppers on 0800 555 111.