Usmaan Mahmood, 20, was found in the street with a single stab wound in Thornton Heath. He was taken to hospital and died early on Wednesday, June 14.
A post-mortem examination confirmed the cause of death as sharp force trauma.
There have been no arrests, and enquiries into the incident continue.
Detective Mike Nolan, from the Met’s Specialist Crime (Homicide), said: “Our thoughts are with Mr Mahmood’s family at an unimaginable time for them. I have assured them that I and my team will do everything we can to bring them justice.
“A young man has lost his life, and it is imperative we identify those responsible. Londoners don’t want violent criminals in their communities and we must work together to remove them from our streets.
DC Nolan added: “We believe Mr Mahmood was stabbed inside Thornton Heath Recreation Ground before running out onto Sandfield Road and collapsing. We are appealing for anyone who may have been at the park at the time of the time to come forward with any information.
“Please do the right thing and call us with anything that could assist our investigation and bring his killer to justice.”