The three letters of my fraternity, TKE, are an acronym for a phrase in greek. Sorry, it’s secret. You won’t get it from me. Most fraternities and sororities that I am aware of the meaning of the letters, it’s the same deal. One fraternity I know of, although I can’t remember which, the phrase is latin, but using greek letters for their acronymic name.
There are still black fraternities, as well as Hispanic, Asian and Jewish ones, although I suspect that today they are open to people who aren’t black, Hispanic, Asian or Jewish. According to Wikipedia, “Alpha Phi Alpha, Phi Iota Alpha, Rho Psi, Phi Sigma Nu, and Zeta Beta Tau were founded as the first fraternities for African-American, Latino-American, Asian-American, Native American, and Jewish students, respectively.”
From my uncle: Puffa Puffa Sig
If you can’t go Greek, go TKE, and if you can’t go TKE… 
There are at least three national fraternities who use Latin mottos but Greek letters.
Still are. The major black fraternities (and sororities) are represented by the National Pan-Hellenic Council. The major “white” fraternities are represented by the North American Interfraternity Conference, and the “white” sororities by the National Panehellenic Conference.
Fun fact: Bill Clinton is an honorary member of (black fraternity) Phi Beta Sigma.
Some of the two-letter societies actually have three letters in their names, but the last letter is kept secret. Others just didn’t bother. The letters nearly always represent a motto, though in at least one case they’re the last initials of the founders.
Others, like Fiji (Phi Gamma Delta) consider their letters “sacred”, though not secret, and print them only in very specific places (or not at all).
My sorority letters also stand for something secret in Greek.
Most Greek organizations with religious heritages came about because of discrimination. The students weren’t allowed in the groups already on campus, so they formed their own. Or sometimes they were allowed in, but they couldn’t vote or hold office. Some of my older sisters told me stories of Catholic women on their campuses who lived in their chapter houses and were served meat on Fridays, and required to attend functions on holy days when it would have been very inappropriate for them to go.
Such discrimination is not legal now at public universities, and many private ones are afraid of the liability, plus the national organizations have no stomach for this intolerance. It does happen on the local level.
My own sorority is about as open as you can get, but the demographics vary by chapter.
“I refuse to join any organization that would have me as a member!”
In Tom Wolfe’s I Am Charlotte Simmons, the snobbish house on campus is the Fraternity of Saint Ray.
Isn’t this true of just about all Greek societies?
My fraternity was Sigma Omicron Alpha Phi, which stood for Student Organization For Alternative Production. Just kidding actually, we didn’t use Greek letters. But the founders modeled themselves after a secret society, and I was a member of the first pledge class of new initiates.
There are also gay fraternities. Delta Lambda Phi is the one I know of offhand.
The letters standing for a motto is, but the motto itself being secret is far from universal. Some of the frat houses around here have the motto visible for all to see on the outside of the house (often incorporated into some sort of seal or other logo).
At my alma mater, a small private school, fraternities/sororities were banned back in the '50s but there were several long-established “secret societies” that had no official status on campus. Several of these had one-letter Greek names. To my knowledge none of the secret societies had multiple letter Greek names. Some had English names and I knew of one with a name that was an acronym for an English phrase.
I don’t think there’s much danger of running out of three letter Greek names. There are 24 Greek letters, and since fraternity/sorority names sometimes use the same letter more than once (e.g. Delta Delta Delta) then there are thousands of possible combinations.
The organizations with open mottos usually have secret ones too.
Funny thing about GDI, I never heard that until I was in grad school. Then someone asked me if I was a GDI and I said I don’t know tell me what it is? When they told me I said I guess I was GDI.
Yes I too studied Latin in a state Grammar school in the sixties(Non optional to start off with) , Greek was only an option for outstanding students.
I have a question related to ethnicity. Among the traditionally white houses, has there come to be much integration, or do African-Americans overwhelmingly opt rush the traditionally AA houses? I must say the prospect of pledging one of the AA houses looks positively scary, based on representations in films and TV programs.
But the letters don’t stand for the secret one. Mine has a motto that is just another acronym on the seal, but an old version of the seal had it spelled out. We aren’t supposed to tell anyone what it is, but a bit of historical research will tell you.
Mine lets in anyone, although I don’t know if it was ever whites only. My school didn’t have any traditionally black fraternities, so all 3 had black members if I recall correctly.