I understand if locals share names with each other without knowing about it, but how can you go on for decades doing so, especially when two of them have a similar purpose (education)?
Check this out:
Phi Delta Kappa (Education Society)
Phi Delta Kappa (HB Education Sorority)
Phi Delta Kappa (regional fraternity)
ETA: Of course, there's Kappa Alpha Society and Kappa Alpha Order