My Arabic is extremely shaky, at best, and my understanding of Arab naming conventions is even shakier. I don’t know anything about how names vary across the Arab world. That said, here goes:
“Al” is simply the definite article in Arabic (the equivalent of “the” in English), but in cases like these carries with it an implied “of.” For instance, one of the most famous prominent plazas in Cairo is Midan al-Tahrir, which translates roughly to “square [of] the-liberation,” or Liberation Square. Think of the second word as an adjective: as we may talk about Richard the Lionheart, we may also talk about Sadaam the Tikriti.
Arabic names seem very similar in form to the way we address letters in the mail: they start with the most specific descriptor and become more general with each successive word. As an address generally goes something like street-city-state, Arabic names generally go from the name of an individual, to the name of that individual’s father, to the name of a larger family or clan.
For example, Saddam Hussein al-Tikriti is Saddam, son of Hussein, of the Tikriti clan. (I’m actually not certain that “Tikriti” is a real clan; I see “al-Tikriti” used all the time in US references to the man, but Sadaam himself never used it and I don’t know my Iraqi clans very well.) Often a name like this would be written “Sadaam bin Hussayn al-Tikriti,” where “bin” explicity means “son of.” “Ibn” also means “son of” (so the famous Arab adventurer Ibn Batuta was “Son of Batuta”), but I believe it’s supposed to change form to “bin” when it’s placed between the names of father and son. A form of this word may also be placed before the name of a clan or tribe, except that it should take the plural form “banu” or “bani.”
It’s possible to add a fourth component to an Arab name: the grandfather’s name, which would follow the name of the father. For example, Sadaam’s sons were 'Uday Sadaam Hussayn al-Tikriti and Qusayy Sadaam Hussayn al-Tikriti.
It’s also common to identify older men and women by the names of their children. You probably heard the old Palestinian prime minister, Mahmoud Abbas, referred to as “Abu Mazan” fairly frequently in the Western press. “Abu” means “father of,” so Mahmoud Abbas has a son named Mazan.
All of the above should hold true for women and girls too; i.e., Sadaam’s hypothetical daughter Fatima would have been Fatima Sadaam Hussayn al-Tikriti. The feminine equivalent of “Abu” is “Umm” (“mother of”), as in “Umm al-Qasr” (“mother of the fort”?).
As for the capitalization of “abd,” Arabic script has no capitals or lowercase and so capitalization in any Romanization thereof is pretty much at the discretion of the writer. “Abd,” as Bromley pointed out, means something like “servant of” or “slave of.” The common name “Abdullah” is probably more correctly rendered “Abd Allah.” There are actually very few other names in which it’s acceptable to use “abd,” and all of them refer to God: “Servant of the Merciful” (“Abd Ar-Rahman”) and "Servant of the One (“Abd Al-Waahid”), to give two examples.
That’s a start, at least.
), would George senior call himself “Abu Jeb”? I suspect so.