Hezion I, son (?) of Rezon is only known from the patronymic given in 1 Kings 15.18. The name, however, appears again with the successor to Hazael in the eighth century, as Hadiānu in the Assyrian texts, which we’ll get to.
Tabrimmon, son of Hezion is also only known from the 1 Kings 15.18 patronymic. The name is a good Aramaic name, Hebraized, meaning “Ramman is Good,” Ramman, Thunderer, being an epithet of Hadad.
Ben-Hadad, son of Tabrimmon is the king of Aram-Damascus introduced at 1 Kings 15.18, during the reign of Asa of Judah (912-871) and Baasha of Israel (911-888), probably toward the later end of that joint period. This Ben-Hadad is bribed by Asa to break a treaty with Baasha and attack him so that Asa can stop a building project of Baasha and steal his building materials. It works. This Ben-Hadad, if he is a separate king from the following one, as seems most likely, is the one king of Aram-Damascus for whom we do not know his personal name. If he is the same as the following, then this is not the case. I tend to think this king is likely a separate one than the following due to the interesting statement in 1 Kings 20.34 in the mouth of Ben-Hadad, an offer to restore towns that his father took from Ahab’s father (Omri or a more distant “father”?), and trading rights in Damascus itself. Ben-Hadad/Hadadezer below is clearly not the Ben-Hadad son of Tabrimmon, as he himself would obviously have been ruling before Omri. If, however, the “father” of Ahab is to be understood as a more distant predecessor, like Baasha of Israel who Ben-Hadad son of Tabrimmon attacks, then the very incident referred to by Ben-Hadad/Hadadezer could very well be this Asa and Baasha incident, as no interactions with Aram-Damascus are mentioned in the admittedly scarce reports on the reign of Omri. The scholarly consensus has moved over the past century from having a single Ben-Hadad throughout, to there being two, though it is apparently still discussed.
Ben-Hadad (Hadadezer) is a long-lived and very militarily active king of Aram-Damascus who has many run-ins both with Israel and Assyria over his long career. He is the Ben-Hadad who battles and finally kills Ahab of Israel in 1 Kings 20 and 22. Some, like Pitard, have taken both chapters to be misplaced from the reign of a later king of the dynasty of Jehu, when Israel was in a much weaker position relative to Aram-Damascus, but a close reading of particularly 1 Kings 20 shows a strong king of Israel bravely opposing outrageous claims. A weak ruler would certainly not win, either, which occurs in this chapter. And while it is set just two or three years before the Battle of Qarqar with Shalmaneser III, and three years before Ahab’s death on the field again against Ben-Hadad, this is not unbelievable, particularly in seeing the back and forth between Israel and Aram-Damascus that continues throughout the history of both kingdoms. This same Ben-Hadad, apparently during the reign of Jehoram of Israel (852-841) besieges Samaria, as described in one of the Elisha tales in 2 Kings 6.24-7.20. This same Ben-Hadad, when ill, sends one of his officers named Hazael to inquire of the prophet Elisha whether he’ll recover (2 Kings 8.7-15). By this time, in the late 840s BC, he’d be quite old, so the illness is of more concern. Elisha tells Hazael that he’ll be the next king of Aram-Damascus. Not wasting time, Hazael apparently smothers Ben-Hadad. This Ben-Hadad is clearly the king of Aram-Damascus known to the Assyrians as Adad-idri, Hebraized as Hadadezer. More details below.
Hazael manages to battle Jehoram of Israel (852-841) and Ahaziah of Judah (842-841) at Ramoth-gilead soon after taking the throne sometime between 844 and 841, based on the Assyrian information (below). Jehoram is wounded in the battle, so he and Ahaziah go to Jezreel, conveniently for the coup of Jehu (2 Kings 9-10). Hazael is also said to have taken all of the Israelite territories east of the Jordan (2 Kings 10.32). Early (?) in the reign of Jehoash of Judah (835-796), Hazael threatens to attack Jerusalem, but is bought off by emptying the treasuries (2 Kings 12.17-18). Hazael and his son and successor Ben-Hadad (whose personal name was Hezion/Hadiānu according to the Assyrian texts, see below) are said to have repeatedly triumphed over Israel (2 Kings 13.3), which isn’t surprising, given the apparent strength of Aram-Damascus at this time when it was even able to take on the Assyrian army and survive despite numerous losses. Hazael is said to have continued to win against Israel through the reign of Jehoahaz of Israel (822-806)(2 Kings 13.22). 2 Kings 13.24-25 seems to indicate that Hazael died early in the reign of Jehoash of Israel (805-791), with Ben-Hadad/Hezion succeeding him, and Jehoash taking back, in three separate battles, all or some of the various towns that Hazael had taken from Israel.
Ben-Hadad (Hezion II) son of Hazael began to reign probably in the very late ninth century or very early eighth, as indicated by 2 Kings 13.24-25. This Ben-Hadad is mentioned in Assyrian texts as Hadiānu, and ruling in Damascus in 773/2 BC. Jeroboam II of Israel (791-750) is said (2 Kings 14.25, 28) to have restored roughly the Davidic/Solomonic borders of Israel, including Damascus (!) in the north and Hamath, and Elath in the south (perhaps ceding it to Judah? 2 Kings 14.22). So, Aram-Damascus was, for at least a time during the reign of this Ben-Hadad, not so strong, despite the statement of 2 Kings 13.3. The Assyrian texts have this king in Damascus in 773/2 BC.
Rezin is the last king of Aram-Damascus. He is attested as ruling in 738 BC in the Assyrian texts, until 732. His accession date was likely quite a bit earlier than that, as otherwise Ben-Hadad/Hezion would’ve had a strikingly, if not impossibly, long reign. He begins to attack Judah during the reign of Jotham of Judah (750-730) and Pekah of Israel (736-731) (2 Kings 15.37), which are likely the same attacks described in 2 Kings 16.5, during the reign of Ahaz of Judah counting his coregency with Jotham (from 735, because his sole rule began in 731, when both Pekah and Rezin were already dead). Precisely because Rezin was threatening Judah, Ahaz of Judah sent to Tiglath-Pileser III of Assyria (745-727) for help, and this led to the elimination of both Rezin and Aram-Damascus in 732 BC. Rezin had, admittedly, been quite a pest to the Assyrians, as well.