From Arabic, via misunderstandings and mistranslations. The name of the star was originally مِنْقَار اَلدَّجَاجَة(minqār ad-dajāja, “the hen's beak”). Latin scholars misunderstood the name to come from a kind of herb, and translated it into ab ireo ("from ireus"). Later, people considered it as a misprint of an Arabic term, and transcribed it as al-bireo.