Why didn't the children of the Rikudo Sennin inherit his surname? As revealed in Chapter 646, the surname from Rikudo Sennin (Sage of the Six Paths) is "Oosutsuki." 

Why do his two sons have different surnames (Uchiha and Senju), instead of inheriting their father's surname?
Taken from the Naruto Wiki:


  His bloodline was divided into the descendants of his two children, which would eventually form the Senju clan — and through distant relations the Uzumaki clan — and the Uchiha clan.