I also do not think that renaming the group is
    practical however much I would love be in the TC GLUG.

Why do you think it is not practical?  What obstacles do you see?

There are many GNU/Linux User Groups, so either they have overcome
these obstacles, or bypassed them, or for some reason those obstacles
didn't affect them as they affect you.  If you explain the obstacles,
maybe someone can suggest solutions to them.

You mentioned these two points:

    However renaming now is a tough proposition and
    overcoming inertia is hard; GNU/Linux (or whatever variant thereof you
    want to use) is a mouthful to say and people will shorten it no matter
    how hard you try.

These statements are both to some extent valid, but neither is an
obstacle to changing the name of the group _if the members decide to
do it_.

The point about inertia is valid in that some people may, from
inertia, cling to the name "Linux" despite good reasons to change.
However, speculating about others' decisions is beside the point now
that the group is likely to have a vote.  The question facing each
member now is not "How are others likely to vote?" but rather "What is
the right decision?"

Is it true that "people will shorten it" no matter what?  Only partly:
experience shows that some do and some don't.  However, the decision
for you to make is not what others will call the system; it is what
your group will say.