They are simply known as Justice League, dropping the "America" on their name. They focus on justice and seeking justice, rather than responding to emergencies, letting the problems come to them, and being almost entirely reactive.
Hal Jordan decides that he wants a pro-active team. This team will go after the equivalent of the FBI's most wanted list, sometimes in different countries, sometimes through time.
The difference is, the Justice League of America is all about the League, it's a family. While this is about justice. It's all about bringing in the bad guys.
Members:
Green Lantern
Green Arrow
Supergirl
Batwoman
The Atom
Shazam
Starman
Congorilla
