are correct. One free name change to get rid of that generated GT. Once you've used that, it's $10 a pop to change your GT. (Hey.. it could be worse. We could get charged $20 or not even have the option for a GT change)
There used to be a way to do this, which included having people report your GT for being offensive, but this has since been patched by Microsoft and will result in a 2 week ban (or maybe even nothing at all) if you try this.
I recommend that you go out and buy $10 in M$ to change it and not try and cheat the system. It'll likely result in you being banned or suspended.