China Airlines is free to change its name to Air Taiwan to really stick it to China (some Taiwanese politicians tried already), but it doesn't because the name change impacts bilaterial agreements and they won't be able to fly to many countries, thus China Airlines keeping its name as a business decision, same conclusion that Air Canada has apparently reached.
While that might have been a factor, I suspect the major one is more related to domestic political issues in Taiwan. I would be very surprised if such a change would ever have been a consideration. Would have been very controversial. For the longest time, people in Taiwan would often pick their favorite airline based upon political consideration. Some still do even if the BR management seemed to have (at the very least) mellowed.