Art of Justice said:
By the way, can anyone clarify what the name of Valyrian steel axe that belongs to House Celtigar is? Also it would be useful to know who currently wields (or at least is supposed to wield) Red Rain (another Valyrian steel sword).
The name of the axe is never mentioned because the weapon itself is merely a rumor, along with other treasures supposed to be hidden on Claw Isle (a horn that summons sea monsters... ). If you're deciding to implement it nonetheless, you'd have to come up with a name yourself.
Edit: I just looked it up. Red Rain is wielded by Lord Dunstan Drumm on several occasions, including the Kingsmoot.