Indeed. To my knowledge, the characters don't have unique IDs even on servers. Rather, they are made unique being of specific name on specific server and tied to a specific WoW account. So, my main propably looks like Trelw-Alleria, rather than Troll Warrior number 2537-Alleria or some such.
Unlike real world, another EU account can't contain another Trelw-Alleria. In reality I have a fairly, but not entirely unique name combination. The only reliable way of separating me from the three? others that (have) exist(ed) on electronical database level, is to look at my social security number, which is unique to me. In fact, long ago there was a mixup as insufficient data was provided and I got confused with another "me", who was just born decades earlier... but even on the same day. Only the last two numbers of part one and the four characters long unique identifier were slightly different.
In WoW, such mixups can't happen. Trelw-Alleria is my alter ego and cannot be duplicated by anyone.
Blizzard naturally tracks more data than what they show us... but you can't see your former names, guilds or realms on Armory, either. WCR offers a very unique way of retaining at least some of that knowledge, but even it requires additional player input.
If characters were truely unique and the system was entirely transparent, there would be problems, too. There are people who get harassed by ex-boyfriends, schoolmates, etc. And some people just plain dislike publicity. That's why the original concept of Real ID, especially on the forums ran into such a storm of resistance. There are people who know Trelw-Alleria is behind his screen, but that data isn't available to all at a click of a button.
Openness and transparency are generally good things, but people should retain at least the option of privacy. Which, in the online environment, is hard. Once something goes online, it won't go away entirely, no matter how hard people try. Of cause, law enforcement agencies, lawyers and judges fight the worst of the problems, like child pornography, identity theft, intellectual property theft, terrorism, etc, but when a bachelor party picture taken 20 or 30 years ago ruins someone's career and marriage, it's pretty harsh... and such things have happened... and will happen.
And on a WoW-related note, there are people who do not hire online players, especially WoW ones. Does the fact that the Norwegian mass murdered Breivik played WoW define all WoW players? No, but it may reflect badly on all the rest of us. Such is life in the digital age...
Safe adventures in the World of Warcraft and happy censusing!
This is the Epic Censi, signing off for now.