Carrel

And in every wyndowe iij Pewes or Carrells, where every one of the old Monks had his carrell, severall by himselfe, that, when they had dyned, they dyd resorte to that place of Cloister and there studyed upon there books, every one in his carrell, all the after nonne, unto evensong tyme. […] All there pewes or carrells was all fynely wainscotted and verie close, all but the forepart which had carved wourke that gave light in at ther carrell doures of wainscott. And in every carrell was a deske to lye there bookes on.

Source: wiktionary

Carol, or Carrel. A little pew, or closet, in a cloister, to sit and read in. They were common in greater monasteries, as Duram, Gloucester, Kirkham in Yorkshire, &c.; and had their name from the carols, or sentences inscribed on the walls about them, which often were couplets in rhyme. [Carola, Low Latin.]

Source: wiktionary

Near-synonym: cubicle (sometimes synonymous)

Source: wiktionary

He was busy writing his report in a small library carrel.

Source: wiktionary