What does "Booney II" mean in this conext?
It is in the name of a product from Columbia:
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Columbia uses this word "Booney" as the name of a type of activewear hat. The style of this particular Booney is "Silver Ridge". This is the second version of the Silver Ridge Booney, hence "Silver Ridge Booney II". Finally, this is the men's version of that hat. It's very common for online clothing retailers to put "Men's", "Women's", "Boy's", etc. in front of the name of the product.
(I thought at first that "Booney" was a trademark of Columbia, but Patagonia uses it too...)
Booney (I'm guessing about this part, of course) sounds like a back-formation from boonies.
Boonies is a short slangy form of boondocks, itself a slang term for remote areas or wilderness - usually used in the phrase "out in the boondocks" - He lives out yonder in the boondocks. - Gee, we're really way out in the boonies here, ain't we?
Boonie-crashing means running or riding through wilderness where there is no existing trail - knocking down, or jumping over, any obstacles. (An admittedly brief search hasn't turned up any official definition, but that's what we called it in high school, and all of the hits I found seem to use it the same way we used to.)
Boondocks itself is derived from a Tagalog word bundok, meaning "mountain"; it entered American usage at or about the time of the Spanish-American War and again during WWII.