The body of Martin Trousdale, 55, was found at his home in Wellgreen Court in the Pollokshaws area at about 5:20pm on Monday. He had suffered head injuries.
Strathclyde Police said that, after a post-mortem examination, the death was being treated as murder. They appealed for any information that could help the investigation.
Detective Inspector Scott McMillan said: "Inquiries are ongoing to narrow down the timeframe of when Mr Trousdale was attacked.
"I would like to hear from anyone who saw Mr Trousdale on Monday, 5 April, or who may have information on his movements on that day.
"Did anyone notice anyone behaving in a suspicious manner? It is important that we speak to any person who could provide that little bit of information that could prove vital to our investigation.
"Officers are continuing to carry out door-to-door inquiries and study CCTV footage in an effort to gather further information on this murder."