Adirael is a demon appearing in Mathers' translation of the Sacred Magic of Abramelin the Mage. Mathers said the demon's name means the "magnificence of God." Although the name is likely construed as belonging to an angel, Adirael is almost certainly a fallen one. He is a servant of Beelzebub. A.G.H.
Belanger, Michelle. The Dictionary of Demon: Names of the Damneds. Llewellen Publications. 2010. ebook.