Well, it is a bit confusing, but Wikipedia isn't too strong on accuracy, either. The history is, Norm Brearley named his new airline, "Western Australian Airways" in August 1921.
He operated for 5 years as "Western Australian Airways" - until December 1926, when the name was altered to the simpler, "West Australian Airways".
The business ran for 10 years as "West Australian Airways", until it was purchased in June 1936 by Adelaide Airways, and the merged company structure was then renamed ANA (Australian National Airways).
"West Australian Airways" is the name the business was most commonly known as.
https://en.wikipedia.org/wiki/West_Australian_Airways#:~:text=Established on 5 December 1921,Adelaide Airways for £25%2C000.