And sometimes they actually write back...

Rico says he sent a (polite, honest, except for a flippant part about whether 'Al' Qaeda, their usage, referred to Alan Qaeda or Albert Qaeda) email to The New York Times, admonishing them on their usage (wrong, in Rico's estimation) of Al Qaeda, and a few other things. Amazingly, Greg Brock, the Senior Editor for Standards, actually wrote back:

Dear Mr. Seymour:

Clearly you have read and commented extensively on issues related to Al Qaeda.  So you are aware there are different renderings of it. Newsweek uses our style. As does Fox News in its postings on its website. The Washington Post uses al-Qaeda. CBS News uses Al Qaeda on its site. The Council on Foreign Relations uses al-Qaeda. I have also seen Al-Qaeda and alqaeda.
A website devoted to Al Qaeda news uses Al Qaeda.
As you know, it means "the Base." So we would not hyphenate those words if we we translated them.  We also drop the "Al" when Qaeda is used as an adjective instead of a noun. (I have noticed, however, that we are inconsistent on this. But that's the challenge of writing and editing two million words a week. There is never a day when all editions of the paper or all postings on the web are perfect. ) Here is an excerpt showing our usage of Qaeda as an adjective; again, we would not write: "to get messages to other the Qaeda leaders..."

American officials described Mr. Rahman’s death as particularly significant as compared with other high-ranking Qaeda operatives who have been killed, because he was one of a new generation of leaders that the network hoped would assume greater control after Bin Laden’s death.
Thousands of electronic files recovered at Bin Laden’s compound in Abbottabad, Pakistan, revealed that Bin Laden communicated frequently with Mr. Rahman. They also showed that Bin Laden relied on Mr. Rahman to get messages to other Qaeda leaders and to ensure that Bin Laden’s recorded communications were broadcast widely.

So to answer your question: you can interpret our style anyway you want to. Alan is good. Albert is okay. But I prefer Abigail myself. Why be sexist in this time and day? (You will have to ask Newsweek, Fox, CBS, and on and on, which name they prefer.)
Even more important than interpreting our style— or even paying attention to it— you get to set whatever style works for your readers, based on your analysis.  That's the way it should be.
Best regards,

Greg Brock
Senior Editor/Standards

Rico says Mr. Brock was being polite, but Al is not a short version of Abigail, no matter what he says... But this is why Rico chooses not to use any English-equivalent forms, but keep it al-Qaeda as in the original transliteration. (And that's how they render the stem 'the' in all the Arab publications he's seen, so joke 'em if they can't take a fuck.)