"The D" is obviously the Entrepreneur. It's been referred as that many a time.
When DS9 got a well-needed add-on in the form of the Defiant it quickly became obvious that Ben And Adam were not going to call it that. For a while they defiantly called it The D, but that didn't feel right. And so The Little D was born.
Is it because the ship is smaller? Is it because the ceiling inside the ship is so low? Is it because they obviously only have the two sets for the ship? Is it because it doesn't have two of the swingingest dicks in Starfleet on it? We'll never know.