Hey guys, long time lurker, just wanted to chime in. Spoiler alert for WOR, WOK, and Mistborn, just in case you have to preface it here.
I thought Odium was definitely the "Broken One," since the Stormfather once stated, "Odium Reigns." So, Broken One=Odium. As for being broken, maybe it has something to due with Odium being trapped/contained on the Roshar system (as alluded to in the letter through WOR)? If Odium wasn't "broken," he would presumably be able to go to different locations, as he has done in the past. So maybe Odium's goal in the series is to become "unbroken," similar to Ruin wanting to be free in Mistborn?