My name is Minnie Wong Qin Qing. If I put Wong as my surname, and the others as my last name, finally the full name will be:
Minnie Qin Qing Wong.
So what can I do?
In terms of booking flights, the only thing you need to consider is what your passport says. It will have fields that are also marked in English, such as "Surname" and "Given names". When you book flight tickets, input exactly what is in those fields, in the corresponding field to what your passport refers to as your "Surname", "Given names", etc.
If that happens to be wrong according to your actual name, local naming conventions, etc, then that is perhaps something the issuing authority of your passport could consider dealing with.
However, in terms of booking tickets, the only thing you personally can do is input everything exactly as it appears in your passport, in the corresponding fields. That is what airlines, governments, etc. will want to see, and the absence of it will typically cause problems.
I agree with other answers here that if this is for an airline ticket booking you should transfer what's stated in your passport to the airline ticket – that is, if this is for international travel.
First name and last name are an entirely western language concept. More generic (and culturally more sensitive) would be to use given name and family name. Since names in China and other cultures put the family name before the given name, first and last name don't make sense here anymore, though I find that many people in cultures with reversed "first name" "last name" are aware of that.
In addition to your purely Chinese name (Wong Qin Qing, seemingly a Catonese/Mandarin mix) in family name – given name order, you also have a western style name (Minnie Wong, whereby "Minnie" is probably the given name you chose) in given name – family name order. When you mix both it could lead to confusion beyond identifying you. So it would be best to be "Minnie Wong" to your western friends/colleagues or in Hong Kong, where that's more common, and be "Wong Qin Qing" or "Wang Qin Qing" in your (mainland) Chinese circle.
I am sure you are Chinese but not China residence, maybe Malaysian Chinese or Singaporean Chinese, am I right? I face this same issue before. Your passport printed Minnie Wong Qin Qing, am i right? Minnie is your Christian / English name. Wong is your family name Qin Qing is your name.
While you make the flight booking, make in this way: First name: Qin Qing Last name: Winnie Wong
Only in this way, while print out your boarding pass, it will show Winnie Wong / Qin Qing, you wouldn't face any problem boarding. This issue actually is suffering many people before, the airline also advice change the first name, last name as formal format Given name, Surname.
Remember, while flight boarding, they only recognize what word type in your passport, if your passport only write as Winnie Wong Qin Qing, don't book your flight with Winnie 黄青青！ But some country passport comes with Chinese Mandarin word and English word, they are safe with both, example Taiwan ROC.
Happy Safe Flight.