Al-Jabr, from where we get the word albebra, is an abbreviated name of the book (The Compendious Book on Calculation by Completion and Balancing). The translator's name was al-Khwarizmi, from where we get the word algorithm. He was of Persian origin.
Oh you're right, I was confused by the rich cultural exchange of translations happening at the time, from Greek and Sanskrit texts to Arabic then later Arabic texts to Latin. Both the book and the author are fascinating subjects I enjoy learning more about.