I never watched the anime of the game, but the Japanese name for that madman would fall flat to the majority of the western audience, whereas Jack has much more significance and technically has the same meaning.
Though yeah, the fact the setting is obviously a Japanese country with Japanese names intact looks a tad weird. Still, it's relatively minor.
Yeah, Genocider Jill was the point I stopped trying to make sense of the story and just decided to go along with the ride. Seriously though, she is brilliant.
Don't get me wrong. I adore the character. But the name just really is jarring/baffling if you're familiar with the original.
For example: Imagine for the US release of Final Fantasy X/X-2 HD they decided Yuna was too Japanese to properly write around for a 30-minute plot point. So they re-named her Susan.
Susan, daughter of Braska; inheritor of the name from Susanalesca.
You're better off making a case with "FFIII" than FFX.