tena koe just a note about your query
if you are referring to Te Rerenoa and Mahu as the parents of Te Oki there are no surnames, this was pre-European, surnames were introduced by the Pakeha. Our tupuna had personal names and these are what have handed down.
i hope this is of some help. if you have any other queries please ask, only to happy to share what I have.
Erueti Korewha