Character names are displayed on leaderboards, but primarily so you can keep track of characters. If you're like myself, and have > 100 characters combined offline and online, having names allows some way to track what character is what. IE. my 1.1.7.1 character is "HAVEYOUSEENMYSHIELD" - so when I see it in the character list down the road, I go "oh, that's my shield bash character."