I have a faint feeling snek is ready to let go of his name and return to his former which might be his only way to regain his power. He already lost it after getting sealed and Dara-san merging with his other half. If his power is still tied to belief to him then sure, another name could work.
But in truth thou, I'm pretty sure he's already tired of everything at this point and pretty much unaware that he's slowly turning something he truly wants to become, being free from all his suffering. Dara-san might be actually the worthy successor of him when his duty was actually to protect the mountain.