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Willfully exposing one's own bare buttocks as a protest, a provocation, or just for fun is called mooning.
A wedgie is pulling someone's undergarments or swimming trunks up through their buttock crack to be hauled over the top of the victim's trousers, sometimes partially baring the victim's buttocks.
It is no coincidence that the English verb to spank is the only one specifically meant for physical discipline of a specific part of the body, and various other languages have terms specifically referring to spanking; in many punitive traditions, the buttocks are the preferential target for painful lessons, from educational to judicial, as offering them for punishment (especially uncovered) adds a psychological dose of embarrassment and even sexual humiliation to the pain, which can be meted out with less risk of long term physical harm than elsewhere. There are, in various cultural traditions, expressions like "seat of learning" which refer to the preferential paining of the posterior in a submissively bent and exposed position.
Many comedians, writers and others rely on the buttocks in these and other ways (such as flatulence and toilet humor) as a source of amusement, camaraderie and fun, despite (or in some cases for the sake of) the risk of being in dubious taste, if not censored.