Obviously more thought should be put into whether they're allowed to brand them in the first place, because frankly, they probably shouldn't be able to... but also this is an excellent use case for being artistic! I bet a local artist (especially the ones with more anarchist or anti-capitalist ideals) would be thrilled to make you new plates, skins, or do art right on-top of your prosthesis and might even be willing to do it for a discount or free as a way to give back.
I've made every dealership remove their emblems from my cars before I signed the paperwork, so I definitely wouldn't be letting a prosthetic company put their logo on what becomes my person. I won't even wear branded shirts, lol.
Logo-free prostheses will be available only on premium health insurance plans. Basic insurance plans will provide prostheses printed with the logos of subsidising sponsors.