How to list my former affiliation when it changed name (and character)
List it as the degree you earned, as it was called at the time you earned it, because that is an accurate reflection of what you studied, and it's what your degree says (or what a verification would say).  If an employer gets to the stage of verifying your degree, you could let them know that the program changed name, but it's not strictly necessary (and they won't always tell you before doing a verification).  

Programs come and go and change names, and whole universities open and close, but even closed programs/universities have alumni and their studies/degrees are still valuable for the knowledge gain (at that time) they represent. 

Even in cases like this one, where credentials were called into question based in part by a school not conferring a particular type of degree claimed, the fact that they historically did (or didn't) could be answered by a simple question and there are opportunities to explain the name change.