Glyn Evans, 52, of Gowerton, was found in the Lliw River near the Kingsbridge Pub at about 1000 GMT on Saturday.
Detectives believe he was due to catch a bus to Scotland and are appealing for information from anyone who saw him on Friday night.
Police said Mr Evans was well-known in the Gowerton area for his distinctive appearance with three gold teeth.
With a post-mortem examination due to be held, police said they were treating his death as "unexplained" rather than suspicious.
Det Insp Simon Davies said: "We have reason to believe that Mr Evans was due to catch a bus from the Quadrant bus station to Scotland on Saturday morning but he never made that journey.
"We need to establish how he came to be in the river and are keen to find out his whereabouts towards the end of last week, particularly where he was on Friday night."
He was wearing black Dr Marten type boots, black Wrangler jeans, a long-sleeved red top with a denim collar and a dolphin motif on the breast. He was also wearing a grey duffle-type coat.
Anyone with information is asked to contact Swansea CID on 01792 456999 or Crimestoppers on 0800 555111.
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