"The Piazza" was written for this collection; all of the other stories had already been published in Putnam's Magazine. So The Piazza Tales is in part a way to highlight the one new bit of the book. Presumably the publishers thought The Piazza Tales sounded better than Hey, Melville Fans! We've Got a New Story In Here!
Melville is Melville though, so there's a bit more to it than that. "The Piazza" is the first story in the collection, and it's a story about daydreaming and imagining and coming up with stories. The last sentence of "The Piazza" says that the narrator is "haunted by Marianna's face, and many as real a story." (1.97) Marianna isn't actually real though, or at least may not be real within the story. The title, The Piazza Tales, then, sets up the rest of the book as possibly real fictions within fictions; you could read the whole book as told by the narrator of the first story daydreaming on his porch, haunted by real fictions, or fictional realities. Trippy stuff, right?