I think the global use for the other fruit is far more dominant, you guys should consider switching to using the term 'Asimina'. Wikipedia says some people call it 'prairie banana', too. I've eaten that somewhere but can't remember where. Not bad, but not as nice as https://en.wikipedia.org/wiki/Annona_squamosa which we get here also.
I haven't heard "paw-paw" in place of "papaya" outside of Asia, so I wouldn't call that global. We're not going to change the lyrics of all our old pawpaw-celebrating folk songs just to accommodate someone else's regional dialect. b^)