The title of this story reminds us that, not only does Walter Mitty spend a good part of his life fantasizing, but that his dreams are very much a secret from the rest of the world. Consider the communication barrier between Walter and his wife Mrs. Mitty. She never listens to him, she has no idea what he's thinking or doing, and she doesn't seem particularly interested. (When Walter asks if it ever occurred to her that he might be thinking, her only response is that she's going to take his temperature when they get home.) By slipping into a world of dreams all the time, Walter also isolates himself from the people around him in the real world.
On the other hand, there's a drama and appeal to the title: this isn't just a bumbling man dreaming; instead, it's a special man with an extraordinary, secret life. Check out "Narrator Point of View" where we discuss the free indirect style of the narrative, or the way in which Walter Mitty's own perspective influences the third person narration. That very same thing is going on here in the title. An objective viewer – like the cop or the parking attendant – would never consider Walter's fantasies his secret life. This title, in a way, belongs to Walter Mitty, because he's the one who sees his fantasies as a secret life, not as mere foolish daydreams.