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).