From what I have been able to find it seems No One Knows how to spell his name.

http://www.csmonitor.com/World/2011/0222/Gaddafi-Kadafi-Qaddafi-What-s-the-correct-spelling

Blame it on the name of the country's head of state, Colonel Gaddafi. Wait, no, that's Kaddafi. Or maybe it's Qadhafi. Tell you what, we'll just call him by his first name, which is, er ... hoo boy.
Part of the problem here is that there's no universally accepted authority for transliterating Arabic names. Normally, news outlets will just go with whatever spelling the subject prefers, but this particular subject hasn't settled on a single Roman orthography for his name.
Instead, Libya's Brother Leader lets a hundred flowers bloom. The banner at the top of his official website spells it, "AL Gathafi." But if you go deeper into the site, you'll see it variously rendered as "Al Qaddafi," "Algathafi," and "Al-Gathafi." Adding to the multitude of his spellings is the increasingly ironically named "Al-Gaddafi International Prize for Human Rights."
And that's just the surname. Variations on his given name include Muammar, Moammar, Mu'ammar, and Moamar, and many others. Once you've settled on how to spell his first and last names, you then have to decide whether you want to add the Arabic prefix "al-" before his last name. Which can also be spelled "el-." And then you have to decide whether the prefix should be capitalized.