Jean-Baptiste is clearly a reference to John the Baptist, which we discuss in detail in the "Character Analysis." But his last name may be meaningful too, and honestly, we wouldn’t expect anything less of Camus. In French, clémence means "leniency." This is ironic, since Jean-Baptiste is anything but lenient in his judgment. (Or, in his words: "No excuses ever, for anyone; that’s my principle at the outset. I deny the good intention, the respectable mistake, the indiscretion, and the extenuating circumstance. With me there is no giving of absolution or blessing" [6.12].) So, yes, ironic indeed.
There’s also clamantis in Latin, which means crying, as in, a voice crying in the wilderness, as in, someone like John the Baptist declaring that the Messiah will come. Again, heavy irony, since in this text there is no Messiah and the voice crying out is that of a man who doesn’t think God exists anymore.
Jean-Baptiste’s profession as a "judge-penitent" defines his character. And in fact, most of The Fall is about defining the term "judge-penitent." This title represents his solution to the judgment-problem – the details of which we outline for you in the Character Analysis.
But there’s also the whole lawyer thing to think about. Remember, Jean-Baptiste was a defense lawyer before his fall. He used to "sleep with justice" every night, or so he thought. He used to "spread freedom on [his] toast" every morning. Part of the reason he found himself to be such a hypocrite is that his profession forced him into a duplicitous stance. By defending the guilty, Jean-Baptiste was implicitly calling himself innocent. This worked great for his ego – until he became aware of his own hypocrisy, a hypocrisy heightened by his choice of profession.