I picked up Guild Wars 2 during the recent sale and just spent the last 30-ish minutes customizing a character, determining his background, his features, all of it. But when I got to the end where I could choose his name, I found that the name I always use in games was taken. Disappointed, I tried my backup name, only for that to be rejected as well. I was so annoyed that I quit the character creation process altogether. For me, being able to use "my" name is a really important part of the experience because it allows me to better connect to my character and the world in which I'll be playing, even though I don't have any interest in role-playing with other players. It looks like Guild Wars 2 allows spaces in names, so I may play around with that and add a last name, but I also don't want NPCs to be calling my character by his full name in every single conversation.
This whole process got me thinking, though - what's in a name? Is choosing a specific name in a game - online or otherwise - important to you? What makes it important? Or do you just hit the "Randomize" button and go from there?