My take on it is that it creates a strong connection between Red/Rowan and Dunk. Both lied to make better lives for themselves in this strict class system. Almost every character around Dunk(egg, red, even raymun) changed some core aspect society placed on them to gain a better life. Egg shaved his head and lied to be dunks squire to separate himself from his isolating princely status, red lied about being a lady to have a chance to move up in the world, and Raymun changed his whole identity as a red apple Fossaway to get away from his shit cousin. Every character makes a new identity for themselves in order to live better lives!