Sinop was founded in the 7th century BC as a trading colony of Miletos, at the northern tip of the region the ancients called Paphlagonia. Its oldest known name is Sinope. The sources say the city took that name either from an Amazon called Sinope, said to have founded it, or from the Sinope of myth, a water nymph and the daughter of the river god Asopos.

The coins argue for the nymph. On city coins of the Archaic, Classical and Hellenistic periods the word ΣΙΝΩ appears as a short form of ΣΙΝΩΠΕΩΝ or ΣΙΝΩΠΗΣ, and Sinope's head is shown on them again and again in different forms through all those periods — which supports the descent of the name from the daughter of Asopos.

Nothing else about the name is settled. Hittite records mention a Sinuwa or Sinuua, but since no Hittite-period material has come out of the excavations at Sinop some writers doubt that the name refers to this place. Another view derives it from Sin, the Assyrian moon god. Some sources argue the earliest form was Sinavur, others Sinip; some historians trace it to a root Sen-ha-pi and others to the Persian sine-i ab, the breast of the water.