The power of Codes and Corruption could not easily be passed on. Gods and Fallen have to give this power and claim the practitioners as their own to wield power. Those who are actual descendants can easily wield power. Those who aren't descendants endowed with power have to take on the name of God or Fallen.
The name was not just for show. The title bestowed on the person was the god or fallen, imbuing the ability to make the known universe submit to it and treat the named individual as part of the power of the great god.
Kyros had no name from Daradiel or is a direct descendant. And yet his memories guided by his wisdom allowed such power.