Henry Stangroom, 21, was found dead at an address in Lavender Sweep, Clapham Junction, on Thursday night, Metropolitan Police said.
A 30-year-old man also found at the residence has been arrested on suspicion of murder. He was taken to a south London hospital where he remains in a stable condition with neck injuries.
The men were found when police forced entry into the address for a welfare check shortly before 9pm.
Police said a post-mortem examination revealed Mr Stangroom died due to stab wounds to his heart and lung.
The Homicide and Major Crime Command is investigating.
Police said they are not looking for anyone else in connection with the incident.
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