HK immigration doesn't care about your boarding pass or ticket. You can enter and exit using your US passport with no problem in that respect.
The problem is that you need to show the airline that you have the right documents to enter your destination country.
Since your tickets are in your Taiwan name, you always need to show the airline your Taiwan passport.
But you can't enter HK on your Taiwan passport unless you apply for an online approval and print it out, whereas you don't need any prior approval to enter with your US passport.
So if you are flying to HK, then you either need to register with your Taiwan passport (in which case you might as well just use it to enter HK), or you have to show the airline both passports and tell them you will use the US passport to enter.
If you are flying from HK to the US, then you won't have a US visa in your Taiwan passport, so you would have to show the airline both passports too. This also applies for anywhere which allows US citizens visa-free entry, but not Taiwan/ROC citizens.
Whether airlines will accept two passports with different names, I can't say.
When departing HK, there is a passport and boarding pass check run by the airport. This is not immigration. It is before you pass through security into the secure area. Exit immigration is after security.
At this boarding pass check, you need to show a passport which matches the name on the boarding pass, which is all they care about. So you would always show your Taiwan passport here and never your US passport. After security, the passport you use at the actual exit immigration is the same one you used to enter HK.
If you are going between HK and Taiwan, then you can still use the US passport to enter and exit, but you won't need to show it to anyone except HK immigration.
Thank you so much for the detailed explanation!! Really informative. Many thanks again!
I could actually use my Taiwan Compatriot Pass (Taibaozheng), but I really want to have a stamp on my either passport, so US seems to be the only choice. Yet my FFPs are all registered under my Taiwan name, and that's why I still prefer to book it with Taiwan name to avoid arguing with ground agents.
It's good to know that HK immigration wouldn't check BP so I can just use my US when clearing border. Thank you so much again for the tip!! ^