🔼The name Bozrah in the Bible
It's not clear how many towns named Bozrah there are in the Bible, but it's either one or two. We hear first of Bozrah as the hometown of king Jobab of Edom, or rather that of his father Zerah (Genesis 36:33, 1 Chronicles 1:44). The prophet Isaiah foretold a great sacrifice to be had by YHWH in Bozrah (Isaiah 34:6), after which He will come north to Israel, wearing garments of glowing colors from Bozrah (Isaiah 63:1).
By the time of Jeremiah, the border between Moab and Edom seems to have shifted somewhat (or there were two towns named Bozrah, which is doubtful) because Jeremiah proclaimed judgment on Moab's cities, including Bozrah (Jeremiah 48:24), which would become an object of horror (49:13), because YHWH would spread His wings against Bozrah (49:22, now again "of Edom", but that's probably just a reference).
The prophet Amos also foresaw the destruction of "the citadels" of Bozrah of Edom (Amos 1:12). And according to the ASV, KJV, Darby and Young translations of the Bible, the prophet Micah proclaimed a restoration which included a gathering of the remnant of Israel like the sheep of Bozrah (Micah 2:12). Younger translations (such as the NIV, NAS and the JSP) read here "like sheep in a pen/enclosure".
🔼Etymology of the name Bozrah
The name Bozrah is a feminine equivalent of an unused noun בצר (bezer), which would probably mean enclosure or fortified city, from the verb בצר (bazar), meaning to separate and protect:
For a meaning of the name Bozrah, NOBSE Study Bible Name List reads Fortress, Sheepfold. Jones' Dictionary of Old Testament Proper Names has Fortification or A Vintage. BDB Theological Dictionary proposes Fortress.