UPDATE: Alum initiation status

[bichonl]

MORE HINTS:
- Three Greek letters in the trademarked name
- Founded at a regular university (not a normal school, teacher's college, finishing school, etc)

[KLPDaisy]

I guess I should read all the hints, right? My second guess is going to be Alpha Chi Omega.

[chitownxo]

Congratulations on finding your home!

I'm going to guess Kappa Alpha Theta.

[bichonl]

More clues:
- The name in Greek letters DOES NOT stand for the OPEN motto
- The symbolism is all Hellenic, not Christian or secular
- The group's purpose was secular, not Christian

[KLPDaisy]

Still guessing AChiO.