In the Islamic tradition, Obadiah is known as Abdullah, which is derived from the name Abdeel, not Obadiah. Abdeel was mentioned in the Masoretic Book of Jeremiah, but not the Septuagint's Jeremiah. In Masoretic Jeremiah, Abdeel was referred to as the father of Shelemiah, one of the men that was commanded to seize Jeremiah and Baruch by King Jehoiakim. If Obadiah’s name was originally Abdeel, then his name would have been changed, as well as his god, from El to Iah, at some point before the Twelve books of the minor prophets were combined in the Persian era. Several other Obadiahs were mentioned in the Israelite scriptures, ranging from the time of David, circa 1000 BC to the time of Ezra the Scribe, circa 350 BC, so the exact identity of the author remains debated.
Nevertheless, the dominant view is that he lived in the 9ᵗʰ century BC, an Edomite who made a lot of money in Samaria, working for King Ahab and Queen Jezebel, and then used his wealth to hide the 100 prophets that the King and Queen were trying to kill. There is some circumstantial archeological evidence supporting Obadiah living sometime before Edom fell under the dominion of the Kushite Empire in the 740s BC. Pottery shards found pottery found at Kuntillet Ajrud, Egypt, near the modern Israeli border, dating back to circa 800 BC refer to “Yahweh of Samaria,” and “Yahweh of the Teman,” meaning Yahweh was worshiped in Samaria and Teman at the time. Temen was mentioned in Obadiah’s writing, and if he was the Obadiah who worked for King Ahab, then he would have probably been a Yahwist.