No, there's no reason for these apart from pointless nostalgia. They weren't even useful or sensible in AD&D, so there's no reason to carry them over into D&D Next.
Characters shouldn't know what level they are.
I vehemently disagree.
See? I'm fuming with vehemence!
Sure, level is an artificial construct for use outside of roleplaying, but at the same time that doesn't mean it has to be entirely separated from it. Part of gaining your name level was the fact that you had achieved, in game, a certain 'level' of prestige, renown, infamy and power. That is recognised by attaining a title. I see nothing wrong with that and think that it only serves to enhance the gaming experience.
I think that having a title every level is probably a bit too much but having 'brackets' of titles would certainly be cool. An additional system of qualification for those levels/titles could also be implemented so that you have to earn the title through an action or requirement in-game. For instance, to be a 'wizard', you might have to be donned as such by a circle of magi who recognise your personal power after succeeding at their challenges. Or perhaps a thieves' guild has to give acknowledge your skill and prowess through surviving their trap-laden gauntlet with the ruby at the end?
A title and challenge every five levels or so seems about right and would certainly add a cool factor to the character and the game.