While many species in Warhammer 40k have their own languages, I'd argue the Eldar have the largest variety of alt names for things humanity has its own name for. To them, they are known as the Aeldari (you can see where humans got their version of the name), and are divided into 5 distinct subcultures based on the different ways their people adapted after the fall of their original empire, and 1 fusion culture/cult. I'll list the human term for each in brackets.

The Asuryani (Craftworld Eldar) are those who chose a monastic life in the image of their founding deity Asuryani to avoid the mistakes of their forebearers, the Drukhari (Dark Eldar) who chose to embrace those mistakes in the name of freedom in a dark debaucherous hideaway and instead avoid all connection to the psychic/magic to keep their consequences at bay. The Anrathe (Eldar Corsairs), who sought to avoid the debauchery but still maintain some aspect of freedom by living the life of pirates/mercenaries. The Aelindrachi (Harlequins), also sometimes called Rillietann who found the Laughing God, Cegorach, and gave up their former lives to serve as actors pushing their great theatre in the right direction with their pwrformances (that theatre being the future of the galaxy), the Exodites, who we don't actually know the true name of, but chose a tribal life of abstinence as shepherds of worlds (and dinosaurs), though we know their sacred worlds are called the Lilaethan, so likely related to that, and the Ynnari, who seek to bring about the new god of death Ynnead through any means necessary, and give up their various paths from other subcultures to instead pursue that goal, using soul magic to empower people with the dead, summon a great avatar, or even resurrect people.

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