The factory tailor is «γαζωτής» [ɣaz̠o̞ˈt̠is̠] (masc. rare), «γαζώτρια» [ɣaˈz̠o̞t̠ria] (fem.) and is literally the stitcher, the worker who operates the sewing machine. The word is a deverbative, from the verb «γαζώνω» [ɣaˈz̠o̞no̞] --> to sew, stitch a denominative verb from the noun «γαζί» [ɣaˈz̠i] (neut.) --> stitch, a Byzantine Greek word, «γαζί(ον)» /gɐˈzi(on)/ (neut.), an Arabic loan قز /ˈqaz:/ --> silk.... There are also archaic words, ie. švelja or švalja. Although švelja would be used for factory tailors. Other synonyms would also be šivač and šivačica.
Also, we have the surname «Αμπατζής» [aɱbaˈd͡z̠is̠] --> tailor of diaconal/priestly/episcopal vestments in the Orthodox Church < Ottoman Turkish عباجی /abaˈd͡ʒɰ/ --> maker of a coarse felted fabric, called عباء /aˈba/ by the Ottomans, ultimately from the Arabic عَبَاءَة /ʕabaːʔa/ --> cloak or jacket made of a coarse felted fabric. The Turkish name for the profession, «αμπατζής» is obsolete, the surname of occupational origin however, is still out there