It would've made more sense if Reese had named the fish Harold, since 'Finch' is a type of bird. In fact, all but one of Finch's aliases so far are birds or bird-related. I remember he has used the names: Partridge, Wren, Crane, Crow, and Burdett (which means 'bird'). The exception was when he introduced himself as a blogger with the pen name "Thomas Paine". I think this is meant to be a pun. When someone asks Reese where he gets his information, he'd mean it if he were to say:"A little bird told me."