> Linux is GPL'ed and the name Linux is also trademarked. But if I decided to port it to run on a lava lamp, what would be wrong with my calling the project "Linux for Lava Lamp"?

You can do this not because Linux is GPL, but because Linus Torvalds has authorized certain uses of this trademark in some form; I could not find specific information for Linux, but the Linux Foundation provides reference: https://www.linuxfoundation.org/brand-guidelines