A Name Claim differs from a Role Claim in that it can uniquely identify the player's assigned/claimed role without actually telling what it does; for example, a Theme Game involving Star Wars may involve the name claim of "Chewbacca". However, the player may not want to mention at that moment that he is a Bodyguard, or 2-shot Vigilante, or whatever.
Name Claims are a special point of danger for moderators as they design the game; if all Townie roles have unique names, it can provide more information to the town in the case of a Mass Claim, and make it harder for Scum to guess what a Pro-Town role's name will be. This danger does not only apply to Theme Games; some Normal Games have been broken wide open by this same strategy. Mods should generally provide Scum with Safe Claims or some method of discerning what a pro-town player's role name would be, unless the game's balance dictates otherwise.