Notice Japanese hardly ever take English names in Japan. It's partly out of chauvinism and national pride, and partly because their names are easy to pronouce and remember in roman letters. AYUMI HAMAZAKI for example. She would never be COCO HAMAZAKI in Japan. But in general, I feel it is a good idea, in this world of globalization and modern communications, for a Taiwanese person to take an English name for business, political or just naming reasons when dealing with the outside world. As someone said above, just easier to remember. Annette Lu and James Soong. Her name in Chinese is easy to remember, LOO SHO LIEN, but Soong's name I can never remember, so I like James Soong as a name.
The younger generation seems into English names, but not the older folks, natch. So just wait a while.
Lee Teng hui did have a Japanese name, Amos, when the Japanese were here. Something like Isao Iwate or something.