I think Kappa Alpha Theta is pretty much universally known as "Theta." The only other nickname I know of is KAT, which we use in a few of our songs, but it's more just to make the rhyme scheme work
On my campus Phi Mu Alphas are sometimes called Phi Mus, probably because our students aren't that knowledgeable about other Greek organizations. I would guess that most people don't even know that there's a sorority called Phi Mu. In general if we're not just calling them Phi Mu Alphas or PMAs, we call them the "Phi Mu boys" though, so I guess the distinction is made in that way.
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