William McPhee, 43, of Clarinda Terrace and Greendykes, in the Inch area of the Capital died on Tuesday night.
Another 41-year-old man was hurt during the incident that took place in a 10th floor flat in the Castleview House block in Gilmerton, Edinburgh at around 8.45pm.
Friends of the men said a fight broke out after a night of drinking and claimed that a third man had also shown up at the address.
A police spokesperson said: “Inquiries are ongoing in relation to his death, any anyone with any information should contact Lothian and Borders Police on 0131 311 3131, or Crimestoppers in confidence and complete anonymity on 0800 555 111.”
