long story short, we're forking a free software. The code is under GNU/GPL license, we've tried to collaborate with the original developer but without success. We're improving the software adding a lot of features and unlikely our code will be merged in the original one.
We want to call the new project with a new name, use the same license of course and change the copyright notice in every file.
I know it should be allowed by the GNU/GPL to modify the code and redistribuite but here some questions:
Sure. In fact, not changing it at least a little would imply it's the original project, which is a bad idea.
You can't remove copyright notices. Add yours on top.
Why do you want to remove the reference to the old project? It's a suggestion, but removing it would be impolite and potentially misleading. The Open Source/Free Software communities value correct attribution.