What does that even mean? The pharmacist is going to ask you why you are taking the drug to decide if they can give you the generic version or not?

Yes. The FDA regulates (among other things) "indications" for drugs. For example, you can't represent that a drug is effective at treating something without FDA approval. So, currently, only one company can make this pill, and even then they can only sell it for a specific list of diseases. After some time, other companies will be able to make the pill and sell it for the same list of diseases, except this one. The FDA has the power to regulate the claims made by various companies, so this was probably a compromise that was part of a larger deal.

Surely there will be two different retail names for it. OldDrug X and OldDrug XLI, or whatever.