http://babynames.net/all/chineseWhen writing traditional Chinese names keep this rule in mind: the family-name goes first. Never the given name.
If you have a guy by the given name Joe with the family name Smith (Joe Smith, in European convention) it'd be written in Chinese and by most East-Asian conventions as "Smith Joe".
You should also keep a mind for syllables. Many Chinese names are a single-syllable long, though you may have doubled-up hyphenated names when transliterated through Pinyin.
And for the love of God, do not use Chinese characters when applying. Transliterate that shit (which isn't as hard as Arabic or Persian where there's no one commonly held or academically "correct" method of transliteration).
I've been writing as China for Precipice of War for five years now. This is stuff I've learned.