I've heard the occasional "Delta."
However, I use "David" myself because I don't know the "officially accepted" terms for each letter, and simply don't care because using that has absolutely no benefit over using something like "David" since the only purpose is communicating the letter, and these do it equally well.
Cheers.
The NATO alphabet seems to confuse some people too. 'David' might cause less confusion.
I know the NATO alphabet and use it because my name is impossible to communicate over the phone otherwise.