Over at [GT], when becoming a full member, our recruits drop their original names (my name since S1 was "mgthree") and the clan members come up with one for them. We usually come up with a couple base on who they are in real life (intrests, occupation, etc) and the recruits can accept or reject them until they have one that fits. Because our names are bestowed like nicknames, it kinda adds that dimension of belonging and acceptance. You become part of something bigger. We've even had a couple of [GT] leave over the years and still play under the 'non-Gen.' part of their name.
Because my name is based on who I am outside of SOCOM it is more personal than an arbitrary name, and I have no desire to change it at all. It really is who I am. Of couse mine kicks ass so that helps.