No, not necessarilly. The gallery name doesn't have to show up on your custom theme - just removing the placeholder token from the template is all it takes. You already did so - http://www.unclealice.com/coppermine/themes/blackbirch/template.html doesn't contain the placeholder token {GAL_NAME}. Read up details on the theming section of the docs.
Thanks for the clarification and I'll study the theming section of the docs. I do, however, disagree with you regarding:
However, this is not related to your initial question and therefore should not be discussed in this thread (we have a strict "one issue per thread" policy that you agreed to respect when signing up).
My question was in response to this portion of your original reply:
[snip]
And while you're at it: give your gallery a name in the corresponding config field - this will (among other things) populate the title tag in each gallery output page, which will be an advantage both visually as well as in terms of search engine friendliness.
You supplied additional information, not related to my initial question, that I was responding to. It seemed to me that a continuation of the discussion in this thread, in order to clearly understand your statement, was appropriate and did not require a new topic posting.
I certainly appreciate the time you and others take to respond to questions in this forum and fully understand the necessity of strict rules and guidelines in order to efficiently provide answers and maintain order. I'll now mark this topic as solved.