At my undergrad campus we called them the Gamma's, never Gamma Phi.

Alpha Sigma Tau has a few campuses where they are just called Tau's, but I would say its only 3-4 of the close to 90 chapters.

For Sigma Gamma Rho, that has to get interesting with Phi Beta Sigma which also among the NPHC uses Sigma.

Regenerating the list
 

Rather than edit the one at the beginning of the page, here is the new list including the changes from the comments. Not sure how to mark Standard abbreviation vs. Occasional

Alpha - Alpha Phi Alpha
Beta - Beta Theta Pi (?),Beta Sigma Phi
Gamma - Gamma Phi Beta, None (Fictional:Gamma Phi Gamma)
Delta - Delta Sigma Theta, Delta Delta Delta(?)
Epsilon - None
Zeta - Zeta Phi Beta , Zeta Tau Alpha
Eta - None
Theta - Kappa Alpha Theta, Theta Phi Alpha
Iota - Iota Phi Theta
Kappa - Kappa Kappa Gamma, Kappa Alpha Psi
Lambda - Lambda Chi Alpha,Lambda Upsilon Lambda, Lambda Alpha Upsilon, and Lambda Theta Phi
Mu - None
Nu - None
Xi - None
Omicron - None
Pi - None
Rho - None
Sigma - Phi Beta Sigma, Sigma Gamma Rho, Sigma Sigma Sigma, Sigma Alpha Epsilon Pi, Sigma Kappa
Tau - Alpha Sigma Tau
Upsilon - None
Phi - None?
Chi - None?
Psi - None?
Omega - Omega Psi Phi

I don't know if it happened at schools other than mine, but everyone referred to Sigma Pi using just Pi.

I had the same thought with Sigma Chi=Sigs.

You can definitely remove the question mark for Beta Theta Pi.

And Alpha Tau Omega, unless you're only referring to the nickname for the GLO and not for members. I don't think I've ever heard ATO called "Tau," but I have heard members called "Taus." For that matter, ditto Sigma Chi and "Sigs."

Sigma Chi nationally prefers "Sigs" as their nickname as opposed to "Sig Chi." I've gotten lectures on this one. :)

A couple of our very old chapters in Missouri go by Alphas, but obviously that doesn't fly at most places.

Yep: either “Sigma Chi” or “Sig”. For what it is worth, I have heard “Sig Chi” used by members and those members also got a lecture.

That is my experience as well. I have cousins who are Alpha Tau Omega members and they sometimes refer to themselves and other ATO members as “Taus”. But I have never heard them (or anyone else) refer to the fraternity as “Tau”.

This may have been a regional thing, but when I was an undergrad at Kentucky, Sigma Nu was referred to as "Nu" and members "Nus". Also at UK, Sigma Alpha Epsilon was called "E" and members were "Es". Not "Epsilon", but the English pronunciation of the letter "E".

To go along with ASTlady, Western Illinois University's Alpha Sigma Tau residence is referred to as The Tau House.

Come to think of it, don't members of Phi Delta Theta sometimes call themselves "Phis" as well as "Phi Delts"?

I have heard just "Delta" used for Tri Delta.

I've heard of Alpha Phi going by just Phi on some campuses.

On our campus, the Alpha Phi members are called Phis and the Alpha Delta Pi members are called Pis! Some people call the Alpha Gams just "Gams" (including some actives :( ) but that is another issue haha! Both the Alpha Phi and Alpha Delta Pi chapters are okay with being called by the single letter name, though I'm not sure if their respective IHQs care for it

^^^Your siggy made me laugh. :)

I have also heard Delta Delta Delta referred to as as "Tri Delta" or "Tri Delt." In college, the Gamma Sigma Sigma chapter often referred to themselves (informally) as "Gamma Girls" but never just "Gammas" though they really could have. There were no other orgs on campus with that first letter.

There is such a plethora of groups that start with Alpha they have to be differentiated somehow. It's either what you described above or English letters.

At my daughter's school, W and L, everyone says "Snu." Since their headquarters is a couple blocks from their house, I guess that passes muster. The SAE chapter has gone by the nickname "E-dogs." I wasn't sure where THAT came from, but just plain E was probably the origin.

My favorite there is still "Guy Phi" for Pi Kappa Phi, to differentiate them from Pi Phi.