alpha Orionis, bright reddish star in the right shoulder of Orion, 1515, from Arabic Ibt al Jauzah, traditionally said to mean "the Armpit of the Central One" (with this arm he holds his club aloft), but perhaps more accurately "Hand of al-Jauza (Orion)." Intermediary forms include Bed Elgueze, Beit Algueze.
Ultimately from an alteration of the Arabic يَد الجَوْزَاء (yad al-jawzāʾ, “hand of the central one”), from يَد (yad, “hand”) + جَوْزَاء (jawzāʾ, “central one”).Jawzā, ‘the central one’, initially referred to Gemini among the Arabs, but at some point they decided to refer to Orion by that name. During the Middle Ages the first character of the name, yā’ (ي, with two underdots), was misread as a bā’ (ب, with one underdot) when transliterating into Latin, and Yad al-Jauza became Bedalgeuze. This was then misinterpreted during the Renaissance as deriving from a corruption of an original Arabic form إِبْط الجَوْزَاء (ʾibṭ al-jawzāʾ, “armpit of the central one”).
A similar explanation is found in the American Heritage dictionary:
The history of the curious star name Betelgeuse is a good example of how scholarly errors can creep into language. The story starts with the pre-Islamic Arabic astronomers, who called the star yad al-jawzā', "hand of the jawzā'." The jawzā' was their name for the constellation Gemini. After Greek astronomy became known to the Arabs, the word came to be applied to the constellation Orion as well. Some centuries later, when scribes writing in Medieval Latin tried to render the word, they misread the y as a b (the two corresponding Arabic letters are very similar when used as the first letter in a word), leading to the Medieval Latin form Bedalgeuze. In the Renaissance, another set of scholars trying to figure out the name interpreted the first syllable bed- as being derived from a putative Arabic word *bāṭ meaning "armpit." This word did not exist; it would correctly have been ibṭ. Nonetheless, the error stuck, and the resultant etymologically "improved" spelling Betelgeuse was borrowed into French as Bételgeuse, whence English Betelgeuse.
jauz : pair [zauj]
From this it would seem that jauz and zauj (also the Arabic word for "husband", one member of the pair), are related through metathesis. This would make them both cognate with the Hebrew zug זוג - also meaning "pair." To me this seems like a pretty obvious etymology: the constellation Gemini, the "twins", was called al-jauza, "the pair." But I haven't seen any sources that take this approach.
Rather, they all claim, as we've quoted above, that it derives from jawza meaning "central." Does that term have any Hebrew cognates?
From the Wiktionary entry for the Arabic root jwz, we see that as a verb it has a number of meanings, including "to cause to travel over, pass through" and "to carry through one's views." As a noun it can mean "main part" or "middle" - both giving us our "central." The connection between "passing through" and "central" is easy to understand - in general, one passes through the middle. The Arabic Etymological Dictionary adds that the verb jaza also means "to divide" (in addition to "go through, cross over, pass along.").
JAram. גְּזַז, Syr. גַּז, Arab. jazza (= he cut off, shore), Aram. גִּזָּא, Syr. גֶּזְּתָא (= wool), Akka. gizzu sha ṣēni (= sheep-shearing, wool). cp. the related base גזה.