As far as naming goes, I agree that "cougar" seems to be the most widely used and recognized name, so it's the one that should be used in game. The various other names could make for some solid Zoopedia trivia, though. Here in South Carolina I still occasionally hear about sightings in the more rural areas, often enough for me to err on the side of "where there's smoke, there's fire" despite the species supposedly being extirpated here, and without fail people call them "panthers".
As far as species vs. subspecies/subpopulation, I'm always going to prefer having the all-encompassing species. The Formosan black bear is a prime example of fixating on a seemingly arbitrary subspecies when just having the broader Asiatic black bear label would've allowed for more played creativity... to say nothing of our brown bear, lion, and tiger taxonomical situations. I'm glad they at least broadened the dhole and babirusa in the final release.