Mike is absolutely right. Call it GNU and be done with it. Solaris, AIX, and IRIX are all Unices. Let Ubuntu, Fedora (which what my youngest calls the G4 even now that it has Ubuntu on) and so on all be GNUs. A veritable herd of them.
Fedora is a “Linux based” operating system in much the same way Mac OS X is a Mach-based OS (modulo xnu), so that’s not a contradiction. 😉
And BSD/Linux just proves the point that it isn’t the Linux kernel that’s important given that it can just be swapped out for another kernel such as BSD’s kernel or Mach. 😉