What is the actual name of this game?

Hi, I've been in this hobby for a few months, I really love it, but there's one thing that's been confusing me the whole time. What's the actual name of this game?

The literal translation of its name (逆転バリバリバース) translates roughly to "Reversal Baribariverse," however, I've also seen the name "Gyakuten Baribari verse" and Bandai themselves seem to call it (when written in english) "Gyakuten Bariba Reverse." Why is this and which name is the correct one?