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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It is. I kind of put my foot in my mouth with the original post title which said that Abdul wasn't a "real" name, and that's obviously not true.
That said Abdul is an interesting last name because it's still not really used by itself in most Arabic-speaking countries, at least not in my experience. Maybe her dad changed his name from something else when he moved to Brazil?