My advice is to immediately rebrand as gracefully and effectively as possible and use all that activist energy to effect the transition.
They kind of have a point which doesn’t make them right, but they hold all the cards and you will lose this one and regret the wasted bandwidth.
This name is pretty rings rather badly in my ears, though I’m not offended by such things. I’d feel similarly if they had named it “fuck sleep”. I’m not offended by the word “fuck” but I don’t really want to buy products that are named that. Do apps need energy drink names to be successful? I’ve noticed a trend in talking about men’s balls in ads, manscaping, underwater fart jokes. It’s seems so much like idiocracy more then something offensive.
On the other hand a rose is still a rose. So I agree they should probably just rename it. I doubt there would be any major loss from doing so.