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.
They don't (the claim is the app promotes drug use, which it doesn't), and it's quite likely that it's a reviewer mistake that will be overturned once the stink on social media gets big enough to reach the right person.
You don't think it could reinforce the idea that Amphetamines could be a useful tool to preserve wakefulness?
The fact remains that in most places amphetamines are an illegal drug when acquired without a prescription.
I think he should just rebrand. A name change is not a big deal, given the app has low name recognition in the first place. News of the rebrand will be the first Google result for people who are unaware of it.
Apple holds all the cards here. There is little to be gained if he wins, and if he loses he will have to rebrand anyway after much wasted effort.