Little is known about Fenrir. He bonded to Tyr at a young age and forged a contract with him to lend him power in exchange for his right arm, which Fenrir is currently housed in. He also has the ability to override Tyr's consciousness and take control of his body if he is rendered unconscious or if his own will is too weak to control Fenrir's powers.
Sol Badguy has a special attack named Fafnir, which also related to the name of an ancient mythical dragon.
Fenrir is named after the wolf in Norse mythology.
It is speculated that Fenrir may be one of the Six Forbidden Beasts like Eddie and Angra, though there is currently no information or evidence to support this theory.
Fenrir is somewhat similar to the Black Beast from the Blazblue series, since it is a powerful creature acting as the protagonist's right arm, much like how the Black Beast rests within the Azure Grimoire, which serves as a substitute for Ragna's missing right arm. They are both also capable of overwhelming their host if their wills prove to be insufficient in controlling their power.