Francis Carolan, 42, was found fatally injured on the landing of flats where he lived in Dundasvale Court, Cowcaddens, at 21:10 on Monday.
Two people were reported to have been involved in a disturbance before Mr Carolan was found. He was treated by paramedics but died at the scene.
Police have appealed for witnesses to get in touch.
Det Insp Mark Henderson said: "It would appear that there was a disturbance in a flat on the fifth floor of 8 Dundasvale Court involving two people which spilled on to the landing. It's there that the man sustained a fatal injury.
"Officers are still at the scene and carrying out door-to-door inquiries in the area.
"I would ask anyone who has information that will help the police investigation to contact Stewart Street Police Office."
Police have released the name of a man whose death at a block of flats in Glasgow is being treated as suspicious.