Character Analysis
The Chairman is the head of the Federated Nations' Investigating Committee, and no, he's never given a name other than Chairman. According the Mannie, the lack of name is because Professor Paz and he are deemed "socially unacceptable" (16.65) as representatives of the supposed Luna Free State.
Providing him with no name also has certain advantages, from Mannie's perspective. Like Mort and Alvarez before, Mannie illustrates the Chairman for the reader not as a person, but as a function, a cog within the clockwork of the Federated Nations. And he's the cog that keeps the laws and rules a spinning.
Law and Order: Committee Unit
The Chairman is all about order and the rule of law; at least, he sure can lay down the law when it goes his way. During the committee hearings, he asks the members to address their comments through him (16.68), which ensures that he controls the conversation. He also demands the meeting be closed to recordings and newsmen. When he finds out that Prof recorded the first meeting, he informs them that the Luna Free State does not control the hearings and so could not set its own rules (17.9). Well then.
Although these committee scenes with him are brief, they all point to a man who uses rules to craft results that are of his own desire.
The Devil's in the Detail
Also, the Chairman is literally the devil. And by literally, we mean figuratively literally, not literally literally. Apparently, there's a distinction now. Mannie sure sees him as the devil at least.
When Chairman takes Mannie into his private office, he offers him the job of Protector Pro Tem of Luna, asking Mannie to convince the Loonies of their inability to win the war, and that the Federated Nations will provide them with free schools, hospitals, and other social services.
Mannie thinks to himself, "He took me up on that high mountain and offered me kingdoms of Earth" (19.52). The line is a reference to a story in the Gospel of Matthew. In this biblical story, the Devil tries to tempt Jesus while in the desert; unsuccessful, the devil takes Jesus to a mountaintop and promises him the world. In the same way, the Chairman is pulling out his devilish bag of tricks and tying to tempt Mannie. So, at least figuratively, dude is the devil.
So let's add this character up, shall we? Without a first name, he is effectively dehumanized by Mannie. Mannie also equates him with the devil, and the man controls the law and rules of the committee hearings. What do we have then? Through the Chairman, we have the novel's representation of government—rules and law fused with the spirit of a corrupting, self-serving devil. Not exactly a pretty picture.