EDIT: Never mind, while you can click in the boxes as if you could edit, it doesn't actually let you type. One of the options if you go to your Play! Pokemon settings is to be listed by first name + last initial. For example, John Smith would get displayed where relevant as "John S.".
Thanks Fony, even though in that topic there was still a good amount of confusion. But the video Darksoulpriest posted I think clears it up. Your Display Name will appear in things like guild lists and such, and there you will see the 4 digit code if there are non-unique names.
I'm not trying to change a character name, though. I'm trying to change the display name associated with my account, the one that ends with numbers and is how others find you in-game? I just started playing again after dropping gw2 shortly after purchasing it, and I didn't realize I'd used my at-the-time-real-life-name as my username until ATt4.