I apologize, I've tried searching through the other posts for this answer and can't find one.

On the General ADMIN panel there is a page titled: Forum Address

There is says you can Quick update your forum name.

Before I do this, does this really mean I can change the name of my forum? So it could be (whateverIwant) .forumotion.com?

The name isn't bringing in traffic like I would like it to so I thought a change of the forums name would help. I just want to be clear that I don't have to buy a domain or something to do this and that I won't loose all my posts on the forum.

If I can't use this to change my forum name please explain how to go about that.

Thank you so much for your time!

You won't lose any data.
Read this tutorial for more information Click Here