It was created by orientalist writers like Lovecraft as an "exotic" name and subsequently popularized in the Anglo literatisphere as a stock Arab character name. doesn't really exist in the Arabic-speaking world as an independent name, even if it's become common in western countries.
It comes from the word "abd" (عبد) in Arabic, which means servant or slave, combined with "ul" or "al" (ال), Arabic's only definitive article. "Al" can also express possession. It's often used as part of theonyms like Abdallah, meaning literally "servant of God," or like Kareem Abd-ul-Jabbar's name which means "servant of the mighty."
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Is it a common shorthand for Abdallah or Abdelrahman or something in Arabic? I have met people who told me that Abdul is their name. Is that just a comfortable nickname like introducing yourself as Johnny if your name is Jonathan or is it an example of being pressured into accepting an unnatural shorthand to make a foreign name easy to remember/pronounce, which is very common here?
My guess is it's anglicization and they just chose to stick with it. A lot of European immigrants did the same thing with their names where some Anglo heard what they said and wrote something similar down.
I think it may be more common in western countries where Abdul has already become a known Arab name. But like no Jordanian or Egyptian person I know has ever used that for a nickname. But Moody for Mahmoud I've heard, or like Dowdy or Doody for Dawood.