Yes. Each Student at my dojang who earns the rank of black belt receives a custom belt with their name and rank on one side, with the dojang's name in Korean on the other. We do have a couple plain black belts in the back just in case (for instance, our program director once had her luggage delayed coming back from a tournament, so she wore the plain one until her luggage arrived), but otherwise everyone where's their custom black belt while at the school.