Now, to truly answer this question, it's important to understand who TerranceTerence Mann is. Or at least, who he is supposed to represent: J.D. Salinger, the American author most famous for writing the wonderful novel: The Catcher in the Rye.
Effectively Field of Dreams is based on a book called Shoeless Joe, by author W.P. Kinsella. In the novel there is no TerranceTerence Mann. All the other characters are there, but not TerranceTerence Mann. Basically, Kinsella, like many others, read and was fascinated by The Catcher in the Rye and became a huge Salinger fan. In fact, he was such a huge fan that he wanted to include Salinger in one of his novels.
To handle this, the film creators made a brand new character, TerranceTerence Mann, with the exact same background as Salinger.