That is different from what was initially said.
Taiwan passport for name of booking, Australian passport to show legal entry into Australia.
This is not at variance with instances where airlines insist on proof of right of entry at destination when one is checking in.
By Chinese name you mean the English (pinyin) Romanized-version of your Chinese name?
Yes my birth name is not in my Taiwan passport, just my Chinese name.
It is not different from what I wrote. I use my Taiwan passport at check in as this is the name booked. I show my Australian passport as I do not have a visa in my Taiwan passport. The airlines know that I do not have a visa. They check this before flights. They would issue me a boarding pass or let me board if I did not have an Australian passport. I leave Taiwan immigration on my Taiwan passport. However if I wanted to I could also leave Taiwan using my Australian passport. This is allowed here as well.
So do catch on. When I arrive in Australia I must by law enter on my Australian passport at immigration. I do not need to show my boarding pass or Taiwan passport on entry to Australia as boarding gates are electronic. They just scan my Australian passport.
oh wow, I have my birth name in my Taiwan passport and no aliases or also-known as. My Chinese name only appears in Chinese characters.
My birth name is not even on my HH anymore. Totally erased. The only thing might might notice if looking at my HH that I was born overseas. But lots of Taiwanese are born overseas.