How should I mention my Chinese professor in a document?
Both 'Professor Liu Yuxin' and 'Professor Yuxin  Liu' are acceptable (apply the first name first or the last name first format depend on the audience). To be safe, just highlight the family name with an underline or bold fond.
It is easier just use the last name 刘教授 (Professor Liu)
You can call your professor 刘雨欣教授 or 刘教授 in Chinese but you cannot call her 雨欣.刘 教授 (apply the English first name first format directly into an all Chinese name)
Edit: capitalize the last name also work