There are reasons. A pen name is an alias. So is your FReeper screen name. (I assure you my name is not "The Cat".
However the form doesn't ask about aliases, but rather other names the person might have gone by. Whenever I fill out security paperwork, I have to add an "AKA", because my father never liked my first name, and always called me by a variant of my middle name. Thus I'm "AKA 'variant'".
In Barack's case he should have at minimum put down "AKA Barry", but also probably "AKA Barry Sotero", maybe Barry Dunham, etc.
So why the name Soetero? Why the surname Dunham? Who was oppressing him that made him decide he had to have a fake name?