The state team was just known as "New South Wales", they had the waratah emblem, but the "Waratah" name was not used at all.
Not to be rude, but - How old are You? I have been following Rugby since the late 70s, and they were always the NSW Waratahs when I watched them.. (Its the QLD Team I can't remember - whether they called themselves the 'Maroons' or the 'Reds')...
In any case, in those days, the only time you were able to pull on a NSW Jumper was for the annual NSW-Queensland Game, or the odd run against a Touring Team - sometimes playing in a 'Sydney' jumper one week, and in a 'NSW' Jumper the next - but in essentially the same lineup.... Using the term 'Waratahs' was not always the primary emphasis back then - but it was referred to as a 'Waratahs Jersey' - if you were picked to play for NSW... Newspapers regularly reffered to 'Waratah Headquarters' when selection time came round each year...
Something has changed in Rugby since professionalism.. these slick marketing-types have encouraged teams to drop their regional names in order to appeal to a wider market - it seems not too bad in Oz Rugby, but in NZ the Crusaders used to be the CANTERBURY Crusaders, the Chiefs used to be the WAIKATO Chiefs, and to be fair - the Reds used to be the QUEEENSLAND Reds - (maybe they still are, in QLD). The All Blacks USED TO BE the New Zealand All Blacks...
The same has happened in NRL and AFL: The Roosters used to be Eastern Suburbs, The Bulldogs used to be Canterbury (Allanhu Akbar)! and The Kangaroos, and Bulldogs used to be North Melbourne and i dunno - was it West Melbourne? Then again... the Brumbies used to be the ACT Brumbies...
The Tahs have always been the Tahs, and tho I wish the commentators would include the past 100 years when they give Win-Loss records between NSW and QLD, they always will be and still Flatter to Disappoint Every. Single. September...