It's not required. My wife has no surname and we applied for TRV's and her PR as such. On travel websites (airlines, hotels, etc.) were they require first and last name to complete the bookings etc., we simply used here name twice. Never an issue. On CIC forms, the official means of doing it is:
First name: NUL
Family name: given surname
Relax, there's no issue! 8)
Her current Canadian documentation (PR, health care, drivers license) lists only one name.