Nomenclature

"Because it is my name! Because I cannot have another in my life."
- Arthur Miller, The Crucible

Your name is your identity. I don't mean your socially imposed designation, some tribal pairing of fad and patrilineage picked for you while you were three neurons short of cockroach intellect, but your true name, the one the devil whispers when he's calling you down, the encapsulation of your personality.
It's no accident that this idea showed up in the Matrix (you know, the scene right after they first wake 'Neo' up?) It is one of the great possibilities of virtual worlds. So what does the average ape do with it in our attempted virtuality, the internet? Calls itself 's00pr-pwnzr', 'badass567' or 'hawtgurl'. This is because the average ape has no identity. Its self-image is completely controlled by societal definitions of masculinity, femininity or social rank.

There are two aspects of identity in online games, accountability and roleplaying. 

For those of us with more than a chimp's self-awareness, the anonymity of the internet is still almost irresistible. The lure of the internet is its lack of repercussions. You log into a game, sabotage your team, cheat, trashtalk, then switch to a character with a different name so that you can keep playing without fear of retaliation. Games, however, are not free of morality. For as long as you are logged into the game, it's the game that matters. Your actions reflect your personality, and no player should be allowed to escape the repercussions for his actions.

The importance of accountability increases with the complexity of the game. It's almost a non-issue in deathmatch FPS games, where your reaction to any player, regardless of who he is and what he's done, is to shoot on sight. It is more important in team games, where you can use different names to avoid letting others remember that you're the one who tends to sabotage his own team. Accountability becomes paramount in persistent world games, and it's no surprise that's where it's been the most heavily opposed.
The reason behind both sides of the issue should be obvious. In a persistent world, you can do the most lasting damage to the highest number of players. Griefers have the highest effect. This also means the majority of players will demand to be allowed to grief without repercussions. It makes them feel big. Companies will pander to this, since it's the majority that's demanding it, but here's what they should really be doing.
First off, it's one account per player, one player per account. Regardless of profit, this rule should be monitored and enforced. Do not allow more than one subscription per credit card or per name, or whatever measures you might need to take.
Second, one character per account. No alts. No switching to your alt to farm elsewhere in the game world when your enemies show up. This implies that MMOs should not be class-based. Replay value should be built into the game itself, not in making players repeat the game with different characters.
Third, the game interface should allow players to track and label each other. If a character goes through a name change, its previous names should be viewable in its notes. Players and player groups should be able to set each others' status as friend, enemy or anything in between using the game interface, so that the idiot who backstabbed you last night can be set to have his name flashing red on your screen. The only anonymity, the only dishonesty, should be that built into the game mechanics: sneaking, invisibility, illusion spells, teleporting.

The second aspect of identity is roleplaying. I will grant that i'm biased. I'm always Werwolfe, Werewolfe, Werwulf, etc. in any game. I create other characters, some which i've actually liked playing, but they're not 'me'. I am Werwolfe. I can't really relate to the usual roleplaying experience, changing identities, becoming someone else for one night. I am always myself, and even though my characters are different, they are only aspects of myself. I can see why restricting players to one name may make them feel constrained in terms of roleplaying in that respect, but then again, that game you're playing is really just a single big roleplaying session. You can still be one person in the world of World of Warcraft, another in Lord of the Rings Online, another in EVE, etc. If it's really that big an issue, force players to kill off their old character in a game before making a new one. If the change is what's important to you, and not the lack of accountability, it won't be that big a sacrifice.
I'm also a bit perplexed by the combined pretense of importance of names and their utter lack of meaning. Roleplayers go to so much trouble in creating identities for their characters, down to creating detailed histories and motivations, but then let their names be chosen by a random generator or some similar external method. Even if you want to be your character instead of having your character be you, your character's name should represent something about him. It should be a nickname. Calling your elf archer 'Alaniliriel Greenleaf' adds nothing to the identity. Calling him 'Quiverless' or 'Barnside' does.

I won't even go into the whole issue of Drizzt and Legolas copycats. They're no better than our old friend pwnzerator457.

Addendum:
I left out the issue of enforced player names. They generally do more harm than good. A player's name gives you information about him. The average leet-kiddie plays like rabid rat and is about as reliable. I should be allowed to spot him as soon as i see his name. To that end, let him name himself 'pwnzerator' instead of forcing him to hide his stupidity behind asome overly-convoluted elvish name that doesn't suit him. Your roleplaying experience won't be damaged any more or less if the cluster of dimwits corpse-camping you and shouting "hyuk-hyuk ur noob we rock u bitch" are named bigdick leftnut and rightnut or Legolas, Aragorn and Frodo.