That is what pissed Ansett off during the 2000 Olympics. Ansett paid huge bucks to be the official carrier, but everyone just assumed QF was. I mean, how could it not have been??
Qantas the International airline is a shell of its former self. If it hadn't "merged" with Australian and been able to utilize that strong domestic income it would have been stuffed long ago.
From 1993:
The Qantas chairman. Mr Gary Pemberton, said the board had agonised over the decision and had considered using the combined name, before deciding that a single brand was the best option.
The proposed name of the carrier has been subject to considerable debate. The managing director of Qantas, Mr John Ward, said that in the end, the international marketability of the Qantas name had proved decisive.
My bolding.
They've since pissed that away in actual terms, but Joe Public still thinks they fly all over the world. Marketing 101.