First name: "Da" is one character and "You" is another. I was named after Dr. Dayou Wu, the great Chinese physicist.
Last name: According to the most recent statistics, "Zhou" is currently the ninth (9th) most common Chinese last name. It is also the name of the first feudal dynasty in China's history. To make things more confusing, I believe it is spelled as "Chou" by people from Taiwan, "Chow" by people from Hong Kong and "Chao" by people from Singapore (if you know of another spelling, please let me know). As for the pronunciation (assuming you don't know Chinese), I'm afraid "jo" is probably as close as you can get.