Nameless - main character, incredibly-focused and single-minded. He's not given to rash action or words. He respects and admires spiritual perfection and clarity of purpose in others, but rejects anything, whether he admires it or not, that does not contribute to his worldview, after having considered it fully. He seems the kind of man who has sacrificed everything else in his life towards the achievement of a singular goal. He clearly believes in the "good of the many" as being an integral part of his worldview, so much so that he is incapable of truly fighting for himself. His "name" is an expression of that; he believes that who is truly doesn't matter, that the particulars of his life are not noteworthy, in the face of his purpose.
Broken Sword - At first, the audience is given to believe that Broken Sword is nothing more than a vain, broken fop. He's an artiste. Broken Sword is petulantly only interested in that which interests and benefits him that is right in front of him. He's supremely selfish, and his lack of desire towards deliberate action seems shaped just as much by his lack of desire to leave his playing as his belief that it will not achieve anything. We learn, over the course of the various narratives, that he is actually far more similar to Nameless than we would have thought: like Nameless, he does not do anything without a great deal of consideration. He's the tired voice of experience, and it's been a painful one. You get the impression that his worldview was dramatically changed in the past (obviously, it was, but I'm trying to keep plot stuff out), and his attempts to rebuild his worldview, combined with a tendency towards introspection and analysis, have greatly contributed towards the hesitancy that annoys his wife. He's holding on to his sanity by his fingertips, but is determined to not let it show, even though he knows he fails in this regard.
Flying Snow - She definitely got a bit of the shorter thrift, compared to the other two, since her character was clearly intended to be a foil for both Nameless and Broken Sword. She's extremely passionate in everything that she does, and shares Nameless' single-mindedness without either his or her husband's introspection. She wants what her life used to be, and is unwilling to let go of it, and sees her husband as both an obstacle to that life and partner in that life. Her lack of introspections contributes to her frustration, which she allows to boil up inside of her and erupt. She's portrayed as very unstable (though less so in her real life than in the initial narratives), and acts impulsively, without thinking.
Also, you forgot the Emperor, who I would actually consider to be the real co-main character of the film, with Nameless. He's guarded and suspicious, but somehow, he doesn't really seem paranoid; he clearly knows everyone is out to get him, and takes comfort in that, seeing it as affirmation of his true worth. He's a classic royal figure - surrounded by thousands, and utterly alone. He craves a level of companionship and friendship that his position denies him, but believes too much in his duty to allow himself to indulge. The audience could wonder how much of this belief is genuine; in direct opposition to Nameless' point of view, the Emperor's is incredibly self-serving. While Nameless assumes that his personal desires are immaterial before his purpose, the Emperor has the luxury of being able to claim that his are the one and the same, and he truly seems to be aware of this. He's not afraid of his own power, but as it increases, he's grown increasingly doubtful of his own motivations. He doesn't just want to be understood by others, he wants their understanding to help validate his own desires in his own mind.
