Just calling it "league" is problematic as that word means other things. Aus and Kiwis are used to referring to it that way, but the sport is huge over there. As Srbin pointed out it would backfire completely anywhere else.
But it does need to be one word.. Kill off union, call it rugby![]()
It wouldn't help the confusion to start, but eventually and with enough marketing it would make Union seem like the smaller code.
Afterall, League has as much right to be called Rugby as Union does.
Oh and call the world cup the Original Rugby World Cup.