Usually names are what other people call you, not what you decided for yourself.
In Europe for example, last names were not widely used during the middle ages, but became important when everyone moved towards the cities.
At that point they just used what was their most prominent feature at the time. My own lastname is of a certain geographical location, that I managed to track down. For most people it's simply the profession of the family head of the time.
For nobles it was almost entirely the land or city they were attached to in the feudal system (firstname of/von/de someplace). I guess it would be the same in this case.