John Kiltie, 44, died following the incident in the town's Park Road at 11:10 on Saturday.
Police said at the time that Mr Kiltie's death was being treated as "suspicious".
A force spokesman added: "A post-mortem examination will take place to establish the cause of death."
Police have said they are following a positive line of inquiry after a man died in a street disturbance in Girvan, South Ayrshire.