DG, DTD, etc… Are the letters significant in any way? Some kind of heraldry? How does a new organization decide what to call itself?
Based on my knowledge about my fraternity, and my understanding about others, the greek letter names of many fraternities stand for the secret greek names or mottos of the organizations.
Because most fraternities have secret rituals, and often the secret name is their most cherished secret, it is unlikely that one can find the meaning behind the greek names.
In a few minutes on the Web, I can find out the deepest secrets behind Scientology, the Masons, and how to make nuclear bomb. Somehow I doubt that the “secret” meanings of a few Greek letters that have been known to thousands of drunk undergrads have remained entirely unknown to the outside world. For instance, according to Wikipedia, “Phi, Beta, and Kappa were the initials of a secret Greek motto, Philosophia Biou Kybernētēs, or Love of learning [is] the guide of life.” I haven’t the time or inclination to look further, but I suspect few are very secret any more.
The math club at my high school had the EXTREMELY secret and hard to decipher name of Mu Alpha Theta. You do the math. 
I rushed a sorority called Sigma Alpha, for Sisters in Agriculture. It was a professional ag. interest sorority. The ag fraternity was Alpha Gamma Rho (AGRiculture). So, some of them do.
Phi Beta Kappa, widely recognized as the first American college fraternity, was at one point a secret society, but has since become open, as well as changing in practice from a fraternal organization to an honor society.
I have no idea whether the fraternal secrets of other organizations are on the internet, and I would be highly disinclined to look out of respect for their organizational privacy and in the hope of mutual respect for mine.
I did a search for my fraternity’s “handshake”, as it were (we don’t call it that,) as well as for some other things considered privy only to those initiated, and I found nothing about them at all. Make of that what you will.
Kappa Iota Phi: the unofficial name of Kiwanis’ sponsored youth program in college. It was KI and worldwide.
But does anyone know the cryptic meanings behind I Phelta Thi, or Tappa Kegga Bru? Or are we doomed to be forever speculating?
The college fraternity ΘΧ (Theta Chi) gets its name from its Greek motto, θηρόποσα Χείρ, or the assisting hand.
We called them the “ox house” even though the letters are wrong; it looks like OX.
The letters of my fraternity stood for our motto. That’s all I’m at liberty to say 
The two that I am familiar with (third-hand through the drunken undergraduate disclosures of others) are surprisingly religious (Christian) in meaning. One strikes me as eye-rollingly presumptuous.
Somebody get Skammer a couple of beers! 