The story
Probably from the phrase "ab ireo" in the title for the constellation Cygnus in the star catalog of the Almagest, as translated by Gerard of Cremona. Christian Ludwig Ideler speculated that "ireo" referred to the plant called irio. Later, people apparently considered "abireo" to refer to the star, and as a misprint of an Arabic term, and transcribed it as al-bireo.
Etymology from Wiktionary, CC BY-SA 4.0.