You’re implying that a group which is a member of a national organization can make their own rules, independent of the larger organization. That is antithetical to the reason for “grouping” in the first place.
But you are right, they would have to use a different name. In other words, they would no long be a unit of the Boy Scouts of America.
A group that is part of a national group cannot defy the rules of the national group. The smaller group can only make rules that don’t conflict with the national rules.
The alternative is to get out of the national organization. Isn’t that what the Mormons are doing?
Is there anything terrible about a group of boys interested in nature, etc., that isn’t part of the Boy Scouts of America?