In the article about Spanish Surnames, Cecil briefly mentions the Vietnamese who seem to suffer from a dearth of surnames with many people called Nguyen.
I always thought the country with the Dearthest (Dearthiest?) surname situation was Korea where over 1/2 of the surnames consist of Kim, Lee, Park, Choi, and Jung. If I remember correctly, they actually had three people with the surname of Park all running for election at the same time.