Sorry if this is a dumb question, but to be clear, you did go to tf2 in the steam store and click install, yes? That's what you need to do to detect an already installed game. It will then go through all the files you already have installed, which might take up to half an hour.
If it doesn't detect the game then you should be able to tell pretty early that it doesn't when it starts redownloading tf2, but shouldn't it then recreate the tf2 folder at the beginning anyway? If it really does require a different name then that will tell you.