Well, this certainly looks like a K’tonian artifact but if you notice the grooves on the bottom, that means that this was actually made on a Jiyong potters wheel as an imitation of the K’tonian style of pottery. This is a replica, albeit a 700 year old, very good replica. I do happen to know a buyer who would be willing to pay you for it.
Patterns in surnames: There are many ways a surname could have evolved over centuries. One possibility is migration. A Roman name may have traveled to France and hence to England where it was later Anglicized. Case in point - the surname Lawrence went from Laurentius (Roman) to Laurent (French) to Lawrence (English) and then to Lowry (Scottish). There is also natural etymological evolution. For example, a Middle English spelling may have evolved to a modern English spelling (e.g. Stiward to Stewart). Where did your character's Surname come from?