Should I put my surname after my given name when I introduce myself?

I'm confused about if I should put my surname after my given name or not when I tell a western people what my name is. I would like to use the Pinyin version of my original name instead of choosing a Christian name as my English name when I communicate with western people. Should I reverse the order? Or is it okay to write my Pinyin name just as it is? If I do, will western people get it wrong and think that my last name is the surname when it's actually my given name.

My suggestion is that Mr. Wang introduce himself as he wants to, which I gather is Wang Xing. But, unless he is OK with sometimes being called Wang (e.g., Hi, Wang!), or when the speaker wants to be formal, Mr. Xing, he explain that Wang is his family name and Xing is his given name. In informal settings, he could say just, "My name is Wang Xing, but call me Xing"

Many Westerners know that the family name first is the traditional order for Chinese names, but many do not. Some Chinese give their name in the Chinese order, and some give their name in the Western order. Furthermore, some Chinese are too polite to correct a Westerner who has gotten their name wrong. In my tennis clinic the instructor called a Chinese lady (women are always ladies in tennis) by her last name and the rest of us by our first names. She had introduced herself to me by her first name several weeks earlier, so I asked her how she wanted to be called, and then corrected the instructor. As it happened, she had put her name on the list in the Western fashion, the instructor knew the Chinese convention, and politely re-reversed what she had politely reversed.

I asked my wife who is Taiwanese (and also has a western name) what she would do. She said that if you want to introduce yourself to a westerner as Wangxing then you should do that. It is not a difficult name to hear and remember so you should have luck with that. For official documents, of course you would put Wang as your family name.

Also, do your friends and family call you Xing? I suspect not...my wife's mom and dad don't even call her by her given name (Chiahui.)

When introducing yourself to a Westerner you can choose how to be called. No one will say "Wait, are you giving me last name first or first name first?" They will accept what you tell them.

"Hi, my name is Xing." "Oh, nice to meet you Xing," or "Hello, my name is Wangxing." "Oh, nice to meet you Wangxing."

My wife says that she would never identify herself using her Chinese name and reverse the order when talking to a Westerner to make it fit their standard. I agree with her.

When editing, my sympathy lies with the person rather than with received convention. You are Wang Xing and presumably have felt Wang Xing since childhood. Those who know you will realise, or may be told, that your family name is Wang and that your personal name is Xing. If the distinction is important, as in matters such as job applications, you should make it clear by explaining. Those who are ignorant of your conventions will try blockheadedly to fit your name to their own conventions by assuming the opposite; they are beyond your help so I would leave your name as Wang Xing.