“Banker
One player should be designated as the banker, who keeps the stock of chips and records how many have been issued to each player or how much cash the player has paid for his chips. Players should make no private transactions or exchanges among themselves; a player with surplus chips may return them to the banker and receive credit or cash for them, while a player who wants more chips should obtain them only from the banker”

it is just called “banker”, but I think you’re right, there’s a special name for it. I couldn’t locate it on a quick search though.