What is the Taiwanese naming order 9surname or given name first)?

In Chinese and its related languages, the family name generally comes first. For example, the former Chinese dictator, Mao Zedong, was referred to as "Chairman Mao," not because people were being rude, but because that was his family name, (Like "Mr. Smith" in English) and everyone in the family had it. Only he, personally, had the given name of "Zedong." In the case you are dealing with, if you are quoting this person from a printed source, you could use the same kind of citation which the original source uses. If not (for example, you are quoting from an interview), it is probably safe to assume that "Hsiang-chu" is the family name. If you are truly worried about handling the matter correctly, check in a library to find how this person is cited in other works, or visit with the instructor and ask for advice.

Most people in Taiwan have a single character surname and two character given name.* In the example you cite of Hsiang-Chu Pai, Hsiang-Chu would be the given name and Pai the surname. Also in Taiwan the convention is that the two characters of the given name are linked with a hyphen when written in romanised form.

*There are some double character surnames and single character given names in Taiwan. However, these are quite rare.