Although increasingly rare, in some countries, especially in Asia, some persons are still known by and addressed by a single name.
If you are mononymous (a person that has and uses only one name) you can still apply to the Green Card Lottery.
Any official government documents you have must corroborate your one-name status. This means that your birth certificate or marriage certificate, passport, government-issued identification, etc. must all show that you have only one name.
On the Green Card Lottery application form, you are given the option to provide your first (given) name, middle (second) name, and last (family) name. If you only use one name, please enter this name into the field for last (family) name.
Regardless of whether you consider your one name as a first (given) or middle (second) name, you must enter it as your last (family) name on your registration.
The same is true for your spouse and any children that also have only one name.