I want to thank all of you for kind comments. The commonly held view is that there was no "Australian" cars prior to the introduction of the Holden in 1948, but between 1900 and 1945 there were many unsuccessful attempts to produce such a car. I hope to feature another one of these attempts in the future.
Getting back to the Besst, I could not find a reason for why such an unusual name was chosen for the car. I can only presume that it was meant to be a pun on "Best".