TBF even here they cant quite decide what to use, there's been periods where they have promoted the game as 'NRL' then periods where they revert back to using Rugby League as the games descriptor. Even now they still say 'play NRL' sometimes when they mean play Rugby League on official stuff.
The change from WARL, NTRL, SARL and VicRL happened in 2013 when the NRl strong armed the independent state bodies into letting the NRL take them over. If they ever took over NSW and Qlnd I'd assume theyd take on the same rebrand.