Name to use on flight ticket

We are taking our daighter back to Ireland for a visit
since she has a Chinese name and English name and we will be using the Taiwanese passport to get out of Taiwan, and her Irish passport to get into Ireland… should we put both her names (both romanized Chinese and English name) on the airplane ticket…

Nah, just pick one. Bring both passports naturally. We’ve taken our son back and forth from to the US/Taiwan several times. Sometimes it’s his Chinese name, most times actually as my wife calls the ticket agency, a time or two in English.

Helps to have the same picture in both passports.