> Does the GPL specify that the user has to change the name when it's forked?
No, in the same way the GPL does not specify the user must use their own computer to develop the fork rather than taking the upstream maintainer's laptop home without asking.
The GPL grants no rights whatsoever to use the name, just the code.
But the GPL grants rights to use the code, which itself contains the name. Is there language in the license that exempts "the source code that contains the project name" from my ability to copy and redistribute it?