Most of the time, I haven't run into any problems. The universities generally don't care since they tend to use full names. I've run into a few people who do belong to both, but I guess each has their own personal system.
Alpha Psi Omega is National and has used the name Alpha Psi Omega for about 4 months longer than we have been using Alpha Phi Omega (see
www.alphapsiomega.org)
At least we haven't had to deal much with confusion with Alpha Pi Omega, which is a American Indian ethnic Sorority with chapters with a few schools in North Carolina.