high, boasting
喬 centers on physical or metaphorical height: something tall, lofty, or elevated. The boasting sense is a natural extension of elevating oneself above others.
喬 is traditionally explained as combining 呑 (a variant of 夭, suggesting a bent or tall figure) with 高 (tall) abbreviated to 冋, together expressing height or loftiness. The exact historical development is somewhat uncertain.
The top 呑 looks like a person stretching upward, and the bottom 冋 resembles a tall gate or frame. Together they show someone reaching high, which can also mean boasting by acting lofty.
For キョウ, imagine a tall person boasting loudly in Kyoto: Kyoto -> キョウ, and the person's elevated voice fills the old capital.