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In Japanese it is Daimaxing. Dai (大) = Big. I'm guessing the localization team thought Die-maxing sounded questionable for the kiddies so they went for something less controversial and "cooler" sounding in Dynamaxing.
The ironic part to me is that the "max" part honestly sounds very reminiscent to "climax" particularly in a sexual sense. Dynamax = Dynamic + Climax. Or for the Japanese variant, Large + Climax.
