Friends List - Character Name vs Account Name?

I have quite a few friends on my list. Sometimes I'll play a public game, and add the cool respectable people I find. Usually when I play with them, I learn their name by their character's name. When they talk in chat and whisper you, it shows their character name. Once you add them, and they're playing different characters, unless you memorized their actual account name, it's quite hard to actually remember who each person is.

Do you guys think that showing your account name in chat, rather than your character name, would make things easier, or do you prefer the character name showing in chat?