Adrax Agatone is the captain of the Salamanders Chapter Third Company. He is also the first Primaris Marine character representing the Chapter and just like every other character introduced as a Primarine in 8th Edition and its supplements, he was formerly an original flavor marine given an upgrade.
Agatone has been characterized as a very steady character, slow to change his mood in a manner that almost reflects Vulkan himself in ways. However, rather than being considered soft for a post-human soldier-monk, he simply cleaves very tightly to a particular set of ideals: If something must be done for the Imperium's sake, it will be done at any cost no matter how bloody - fitting, given the 3rd Company is deployed specifically into situations where the Salamanders have no choice but to sacrifice innocents for the good of the Imperium. This has seen him pitted against a number of other demagogues and manipulators, all twisting this ideal of working for the sake of the Imperium's survival. Unlike them, he sees it as a terrible but necessary duty that must only be undertaken as a last resort - he may be ruthless and pragmatic, but he is still a son of Vulkan at heart.
On the Tabletop
Agatone stands as a basic Primaris Captain, but he retains a level of versatility most of his contemporaries might have missed out on. Alongside the basic rules of his station, he gets Unto the Anvil so fellow Salamanders within 6" gain +1 to wound with melee weapons if they charged or performed a Heroic Intervention. This - together with his damage 4 hammer - makes Adrax monster in close combat. He has 58% of killing Leman Russ tank on the charge. 86% if you spend 1CP. Pair him with Bladeguards, Lieutenant in Impulsor and watch them do tremendous damage. He also has the Arridian Drakescale Cloak, which reduces all damage suffered by 1 (to a minimum of 1), which adds a good deal to his durability.
Offensively, he has two weapons. The Malleum Noctis is a one-handed Thunder Hammer which only adds an extra point of damage to the basic weapon statline, which is fine enough since it's already flattening most things it's used against. He also has Drakkis, a Hand Flamer with 12" range,S4 and AP-1, both quite helpful against mobs.
In the Fluff
Agatone was introduced in the book Salamanders as a senior Sergeant in the 3rd Company. He gets promoted to Captain at the end of the book. He gets a lot more page time in the second book, Fire Drake, wherein we get to see how he interacts with living legends like Vulkan He'Stan as well as common mortals.