I really don't know Chinese but I just started to study in China online. I am preparing a report and I need to mention my professor's name. In Chinese it's written as 刘雨欣(liuyuxin), this means 刘(liu) is her surname. Should I write Professor Liu Yuxin or Professor Yuxin Liu?
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
Just to supplement, you may ask if your professor has a specific preference / or is famously known for her name in the Western or Chinese order. Consider Lee Kwan Yew (李光耀), but Yo Yo Ma (馬友友).
There may also be a good justification to adopt the Western order, especially if your professor's work needs to be cited in her surname. E.g., Yitang Zhang (張益唐) is a mathematician who developed groundbreaking work in the field of number theory, but there were subsequent improvements on his work. The academic field may therefore need to use the Western order for its members to unambiguously and correctly cite his work as Zhang's work.
Wikipedia concludes several rules of thumb which you may find useful.
Besides Tang Ho's suggestion, you may also capitalise the surname, as in 'Yuxin LIU', but that may be unnecessary.