Well, good question. I hate to dump a Wikipedia answer on you, but the site does point us in an interesting direction:
In 1986, Gaddafi reportedly responded to a Minnesota school's letter in English using the spelling "Moammar El-Gadhafi". The title of the homepage of algathafi.org reads "Welcome to the official site of Muammar Al Gathafi".
The article also references The Straight Dope, a mainstay fact-finding and generally informative and entertaining column written by "Cecil Adams" for The Reader, my hometown's free weekly, which elaborates on the issue. In it we find this bit of corroborative information:
How Should We Spell Gadhafi?
Well, there's no real right answer. However, the Straight Dope provides some sound advice. It notes that it is a general rule of thumb that if there is doubt over how to spell a person's name, you simply use the version that the person in question uses. In this case, it's a bit tricky since Khadafi spells his name in Arabic.
However, the Straight Dope points out a strange incident that sheds some light on this issue. Back in May, 1986, Kadafi wrote a letter to a class of second-graders in St. Paul, Minnesota. Underneath his Arabic signature was typed "Moammar El-Gadhafi."
[Emphasis my own]
The Wikipedia article also notes the difficulty in standardizing Arabic names:
Because of the lack of standardization of transliterating written- and regionally-pronounced Arabic, Gaddafi's name has been transliterated in many different ways into English and other Latin alphabet languages. Even though the Arabic spelling of a word does not change, the pronunciation may vary in different varieties of Arabic, which may cause a different romanization. In literary Arabic the name معمر القذافي can be pronounced /muˈʕamːaru lqaðˈðaːfiː/. [ʕ] represents a voiced pharyngeal fricative (ع). Geminated consonants can be simplified. In Libyan Arabic, /q/ (ق) may be replaced with [ɡ] or [k] (or even [χ]; and /ð/ (ذ) (as "th" in "this") may be replaced with [d] or [t]. Vowel [u] often alternates with [o] in pronunciation. Thus, /muˈʕamːar alqaðˈðaːfiː/ is normally pronounced in Libyan Arabic [muˈʕæmːɑrˤ əlɡædˈdæːfi]. The definite article al- (ال) is often omitted.