Victim Gerd Michael Straten, 59, is thought to have been living on the street for several years, police in Rhineland Palatinate told press late on Wednesday evening.
Police said Straten had been sleeping regularly in the central grave yard where his headless body was found.
He was often seen walking during the day in the centre of Koblenz, a historic university city on the banks of the Rhine river.
The victim was last seen alive last Thursday near Saarplatz not far from the river, police said.
No suspects have yet been identified in the case, which is being investigated by a special commission.
Police are appealing to the public for further information.