At Otterbein , we have Pi Kappa Phi (country club) and of course there is the national Pi Kappa Phi. There was at one time a dispute over the name, but I'm not sure how it was resolved. The two don't share anything similar at all. They use country club (club for short) more than Pi Kappa Phi.
But also, Sigma Delta Phi (sphinx) was founded as Delta Sigma Phi, same as the national fraternity. At one point and time the national offered them the chance to affiliate, but the brothers decided against it and continued on their way. Sphinx has gone through many changes, their history is one of the more "colorful" on campus.
ETA: Sphinx history
http://www.sigmadeltaphi.org/history/history.html
Pi Kappa Phi (Club) website
http://www.occountryclub.com/site/index.php
(which they've redone recently, and I must say it looks pretty awesome.)