It shouldn't be a problem, since the other Kappa Gamma Delta groups are local/regional and not in your area.
IMO, locals should stay away from the letters of NPC, NIC, NPHC, and other inter/national orgs, and locals/regionals at the same school and possibly also in their geographic area... but there are only so many 2- and 3-letter combinations of Greek letters out there... eliminate the ones that don't stand for anything meaningful, and the ones that spell odd things (who'd want to be known as Alpha Sigma Sigma?

) and you have even fewer options.
How is Kappa Gamma Delta / whatever doing these days?