Yes, if your fathers name and now your surname is something like Hasan then you do not have a chance of taking that name as a surname as it is a first name. If your father has not already taken on a family name then you have the option of sharing the same surname as any of your amcas/uncles or else you find something original and adopt that.
Your documentation outiside of the TRNC can remain the same as you will register your old surname against your new one but anything in the TRNC will have to be in your new surname.