The irony is twofold here. Firstly, it is shown during his interrogation of Hester as he tries to make her confess as that is the best thing to do, but also praises her when she does not. Secondly and most importantly, reverend Dimmesdale is the father of Hester's child the very one whose name he has to find out. This is a good example of irony in the novel as the good reverend is, on the surface, an ideal minister, but on the inside he is being eaten away by his conscience.
