The texts of the Assyrian merchants from the early second millennium, found at Kanesh, in the center of Anatolia, showed that Zimishuna was not far from Durhumit. For example, a letter from a merchant came to Sinahuttum says he keeps his donkeys to sell its remaining wool at Tamniya, he says the town is closed, before returning to Zimishuna, which latter appears, therefore, as another port on the black Sea.
The phonetic proximity between Zamishuna and Samsun is obvious.
Amisos classic is the tell "Tepe Toraman," northwest of the modern Samsun, because a Byzantine mosaïc was found there. This is the town founded by the Milesians during 750 BC, probably with the help of the inhabitants of Phocaea. The Greek historian Hecataeus wrote that Amisos was once called Enète.
This opens a possible new name for the ancient tell "Dündartepe Höyüğü" located south of Samsun. From 1940 to 1941, excavations were carried there by the professors İsmail Kılıç Kökten and Nimet Özgüç. They show an human occupation from the Chalcolithic to the middle of the Bronze Age. The archaeological layers of the time of the Assyrian merchants, as well as those of the Hittites were clearly identified. Copper and bronze have been found.
On Internet there is a Greek justification of the name of Samsun which does not seem convincing. It seems rather result from a development of the present city around "Dündartepe Höyüğü" rather than "Toraman Tepe". Those ancient names were transmitted by successive generations of men who inhabited the area.
My notes of veracity :
4000 years ago, Zimishuna was the name of the present Samsun: 3/5
3600 years ago, Zapishuna, or Zamishuna, was the name of the present Samsun: 3/5