God forbid if your last name has a space in it in your passport (MC DIRMID). The fun in China will never end with that. Also, your middle name is now a part of your first name, sigh.
On the other hand, reverse roles for a second. Try opening a bank account in a Western country with a real Chinese name and you don't even get to the "fun" part. We have to put up with some language gotchas; they're forced to invent an entire new name.
If you're Chinese and find yourself in the West, you spell your name in Pinyin. You don't have to invent a new name unless you want to (I know a Chinese person who did this, but it was for social reasons, not necessity.)
On the flip side, you definitely should invent a new name if you're from the West and want to live in China for a extended period of time, or you'll find that life can be very painful. Sometimes you can even find a direct translation, e.g. David => 大卫 (Da Wei).