Renaming something isn't the same as claiming ownership. As sjp has said you can fork the project, at which point it is a good idea to change the name to avoid confusion. I agree that doing this to just have a new name is extremely lame but it's not disallowed.
Forking and renaming, and then adding features later would be fine. Technically this is what you would do anyway because you need two different names for the two projects in your project directory.
But bear in mind that you will have to include the original copyright notice and that all your changes will have to be GPLd.
There's also nothing wrong with packaging a number of projects into a single package and distributing that under a different name/brand. This is, after all, what every Linux distro in the world actually is