Many airlines have their own callsigns/nicknames/whatever for use over the radio. A British Airways plane is called "Speedbird", US Airways is "Cactus", etc. So why doesn't Delta Airlines do the same? It would seem to need one a lot more than others, since "Delta" is the NATO Phonetic Alphabet name for "D", so it would seem to present a huge potential for confusion.
Atlanta airport, Delta's headquarters, uses "Dixie" for the letter, specifically to avoid confusion with the airline. It just seems easier and safer to me for the airline to adopt a callsign rather than deviating from the phonetic alphabet.