Many airlines have their own callsigns for use over the radio. A British Airways plane is called "Speedbird", US Airways was "Cactus", etc. So why doesn't Delta Air Lines 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.