Noticed on TV Tropes's page for Kamen Rider Ryuki that the only entry under Kamen Rider Odin's character sheet discussing his name origin (that of Odin of Norse myth) just says "He's named after a god, which rings true considering just how overpowered he can be."
This is true, but I'm here today to say that it goes so much further than that, which I've realized while reading/re-reading the Prose Edda and Poetic Edda.
In the Grimnismal, Odin in disguise as the titular Grimnir gives a list of his numerous names and titles. In particular, Grimnismal 48 has him list "Battle-Merry" and "Battle-Stirrer" as two of them. Both titles point to Odin being a god of battle/war, the latter indicating that he stirs up war. In Ryuki, Kamen Rider Odin is meant to be the Rider stand-in for Shiro Kanzaki, who instigates the Rider War. He notably does this by approaching different people and giving them their Advent Decks, thus stirring them to engage in battle with the other Riders.
One of Kamen Rider Odin's cards is also the Time Vent, which rewinds the events of the Rider War back to the start, erasing everyone's memories (though Shinji manages to hold on somewhat, as shown little more than halfway through the show). This effectively puts the Rider War in an endless loop of Riders fighting, dying, and coming back to life to fight again. Those vaguely familiar with Norse myth may have heard of Valhalla, and of the Einherjar. In Vafthruthnismal, the giant Vafthruthnir describes Valhalla's daily battle as this:
"All the Einherjar in Odin's hall fight each other every day. They kill each other, but then ride back from battle and sit in the evening as friends." (Vafthruthnismal 41)
Valhalla's battle is thus a cyclical one, in an endless loop until Ragnarok. In a way, you can call it one of the oldest examples of a battle royale like the Rider War, with the same fighters dying off only to be brought back to life to fight another day. The Rider War can even be seen to parallel Ragnarok, with how the ultimate end of the war is the winner's ability to rewrite the world as they see fit, much like how Ragnarok is meant to end with the destruction of all the gods, only for a new world to be born from it. Indeed, Odin's whole reason for having battles is to gather warriors for Valhalla--like how Shiro keeps engineering the Rider War for his own goals.
So yes, Kamen Rider Odin is a very appropriately named Rider...
