How do you name a frat/sorority?

The letters are derived from the secret greek motto of the group. Only members know the motto. For example, Phi Beta Kappa started out as a literary society and social fraternity before becoming an honor society. They allow their motto to be public. Phi Beta Kappa (ΦΒΚ) stands for Φιλοσοφία Βίου Κυβερνήτης or philosophia biou kybernētēs — "Philosophy is the guide of life"