Kastamoni (Byzantine Kastamon) is the name of a city and province in Turkey today called Kastamonu but also referred to as Kastambol or Kastambolu. Another city in the province is Inepoli (Tr: Inebolu). Kastamoni is not within the borders of most maps depicting the historic region of Pontus.

The city is located at the base of a mountain at which a Byzantine fortress existed. Many believe that Kastamoni was originally called 'Kastron Komneni' (Kastron meaning castle in Greek and Komeneni referring to the Komnenos Empire of Pontus). 

The Kastamoni Castle (Tr: Kastamonu kalesi) Source

Prior to 1923 and the exchange of populations, Kastamoni had a population of 1,800 Greeks. Anna Comnenos refers to Kastamoni as the 'father city' in The Alexiad. From this many inferred that Kastamoni was the fatherland of the Komnenes. 
Source: The Encyclopaedia of Pontian Hellenism