Dragon Magazine on Illithid, issue 308
Armed to the tentacle, The Illithid Arsenal
This issue is mostly about symbionts! One of my favorite illithid items, which has since mostly been dropped from the lore, or at the very least, shifted to being a General Thing, at least as far as the wiki for them goes. This issue also has one of my favorite illithid depictions and inspired me to make my oc Diadem!
By any other name, races of the Underdark
Very little actually about mindflayers in 281, but it does have personal names. Do keep in mind that this issue has been seen by many people, so if you do plan to use them to name your character, be aware that you might eventually come across another illithid with the same name.
Other books that have mindflayer lore:
Phandelver and Below: The Shattered Obelisk
Dragon Magazine 308 (you are here)
Dragon Magazine 281 (and here)
The Illithiad [BW - Color] (This ones my fave :)) (part 0)
A Darkness Gathering (Part 1)
Masters of Eternal Night (Part 2)
Dawn of the Overmind (a lot of bg3 is based on this book) (part 3)
Murder in Baldur's Gate (this is where the emperor came from)
Waterdeep: Dungeon of the Mad Mage
Van Richten's Guide to Ravenloft
Mordenkainen Presents Monsters of the Multiverse
Fizban's Treasury of Dragons
Psionics Handbook [Basic - Extended]
Monster Manual 4th edition
Lords of Madness: The book of Aberrations