The Poet is a welcomed—well, more tolerated than welcomed—guest of the Leibowitz Abbey during Dom Paulo's tenure as abbot. He has a way with words. And by that, we mean he twists and bends them to make jokes, usually at the expense of someone else.
Believe it or not, this makes him a particularly Shakespearian chap.
The character of the fool is usually a court jester or traveling entertainer who sings songs and tells jokes. But in those song and jokes, the fool keeps it real, telling the members of the court what's really going on around them.
Those not in the know believe the fool is just kidding around, because they don't comprehend the joke's intricate wordplay. Those in the know—usually the audience more than any of the play's characters—understand the fool's wordplay and see that the "fool" is actually smarter and more observant than most of the other characters.
If we had to pick one of Shakespeare's many fools to compare the Poet to, it would be the Fool from King Lear. Like that famous court jester, the Poet's jokes center on politics and social commentary. And he's not afraid to tell The Whole Truth, even to his social superiors, who are apt to punish him for his honesty.
If only they understood what was happening.
As with Shakespeare's fools, the Poet's jokes are exclusive affairs—some people understand them, and some people don't. For example, the Poet jokes about Taddeo's guards taking up sketching, and how their "drawing of the underwall tunnels will be hung in a museum of fine [art]" (20.56).
Thon Taddeo thinks this is just a bad joke, but Dom Paulo realizes the Poet is actually referencing how the guards are spying on the abbey's defensive strengths so that they can report back to Hannegan.
You could also consider the Poet's joke about his removable eye. The monks called the glass eye "'the Poet's conscience,'" and the Poet went along with the joke. With his eye in, the Poet would not allow himself to drink from a wine bottle, no matter how much he wanted to. Then he'd pop the eye out, and be perfectly fine with drinking wine. Or pouring it over his head (21.48).
The "joke" here is that most people have the ability to turn our morals on and off, just like the Poet can pop his eye in and out. As Dom Paulo notes, the Poet would take it out "'whenever he saw something that displeased him, when he was pretending to overlook something, or when he wanted to play stupid'" (21.47).
This is exactly what Thon Taddeo does when he overlooks Hannegan's immoral political schemes. It's also the same thing Hannegan does when he tortures and murderers poor Marcus Apollo before declaring the Pope a heretic.
But this time, Thon Taddeo does understand the Poet's joke, and so he takes the eye to Hannegan. In perhaps the most hilarious part of the book, we learn that the eye becomes a sort of relic in Zerchi's day.
And the Poet? He's declared a saint. Now that's comedy.
The Poet isn't given a proper name. His name simply reflects his occupation, or, at least, what he claims to be his occupation. We never actually see him write anything, and the lone book bearing his name might not have been written by him (27.82).
The Freeloader might have been more apt.
This naming convention follows that of many of Shakespeare's fools, who are named for their occupations, too. Several are simply called "fool" or "clown" in the play, but the Gravediggers in Hamlet and the Citizen in Julius Caesar are good examples of non-jester clown characters.
Once again, if it was good enough for Shakespeare, then it's good enough for Mr. Miller.