Usually, when I introduce myself, I'd go "Hi, I'm ZUO YI", deliberately emphasising the pronunciation. The replies I get? "Do you have an English name?" For the first few times, they will try to get the pronunciation right, then it finally settles into the more common forms I have been called.
The worse scenario is when people think that I am a guy based on my name alone (if they have not seen me before).
For so long, I have refrained from giving myself an English name. Finally, I have decided.