I think the site should be renamed to Unix family, instead of the rather dull and arrogant Unix & Linux. It's like saying Linux and Ubuntu instead of Linux family (if the site was just for Linux systems).
The advantage of “Unix and Linux” is that a lot of the potential audience has heard of Linux but not of Unix. And it's short and flows well, unlike the more correct “Unix including Linux” or “Unix, Unix-like, Unix-derived, Unix-emulating, Unix-simulating, Unix-inspired, Unix-resembling, Unix-flavored, Unix-shaped, Unix-tasting, and/or otherwise and without limitation Unix-y systems, including, but not limited to, Linux, GNU/Linux, Lignux, GNU/X11/Linux, GNU/X11/Apache/Linux/TeX/Perl/Python/FreeCiv, and other systems that may contain Linuts”.
Granted, this argument could be stretched to mean the site should be called “Unix and Linux and Mac OS X's non-GUI bits”, but that would be a bit long.
“Unix and Linux” might be taken to imply that non-Unix-like Linux platforms (e.g. Android) are on-topic. This hasn't been decided yet, although the lack of questions can be interpreted as saying they're off-topic.
I disagree with you. This is nitpicking and is not actually a good brand (personal opinion).
In any sense... you should probably post your suggestions on the elevator pitch thread which is exactly about our branding... If you'd like to pitch it, that's the correct place, as opposed to starting a new thread.