Delta Omicrons go almost exclusively by "DO" 's. (each letter said seperately, not the word "do" which often confuses our NMs.
We did recieve word from Inter/Nationals my senior year of college that "referring to Delta Omicron by anything less than her full name was not to be permitted", but.... yeah, that didn't take.

That's a lot of syllables to yell out across campus
On the Phi Mu Alpha Sinfonia thing... I went to school near GeekyPenguin, and the Sinfonians referred to themselves almost exclusively as "Phi Mu's". Occasionally you'd hear "Sinfonian", but that was rare. Phi Mu was the nickname they preferred.
Other chapters on my campus (ie. what the chapters called themselves):
Alpha Sigma: no nickname
Delta Zeta: DeeZee's
Sigma Sigma Sigma: Tri-Sigs (though I've since learned here that most chapters don't like this)
Tau Phi Lambda: Tau Phi's
Pi Kappa Alpha: Pikes
Delta Chi: no nickname
Lambda Chi Alpha: Lambda Chi's
Phi Chi Epsilon: Phi Chi's
Phi Sigma Kappa: Phi Sigs
Tau Kappa Epsilon: Tekes