You're asking the wrong questions because you're mixing up copyright and trademark law.

The GPL covers copyright. It includes the source code, which as you noted contains the project name. This is why you may click "fork" on GitHub and wind up with a fork that is "yours" under the original name.

Trademark law is usage based. If you then set up a website for your fork under the original name, that's illegal. The fact that you're allowed to have a fork containing that name isn't relevant. Copyright allows the code, but you're now violating trademark law.