The only thing that is different in the "Steam" folder when you have serveral accounts, is the "userdata" folder or something. "call of duty modern warfare 2" folder is the same exept "player" folder, but that's kinda irrelevant. So if you have mw2 installed on your first Steam acc, you don't need to download it one more time. Just put the aIW files in the game folder "common/call of duty modern warfare 2".
Edit: Think I might misunderstood your question. But I don't understand what you mean with "I still only have my new account name in my steam folder". Cause you can't read your Steam name anywhere in the steam folder.