How can I add the og to a menu when a new organic group is added? I want to create organic groups that represent counties, and have a menu with some states already Set up, so the user can just select the state for the organic group to be listed under.  The title of the organic group will be the name of the county, which should be the same as the link in the menu.

Is there a way that this can be set up when the organic group is being created?

I'm using the latest release of drupal 6, and organic groups 6.x-2.1.

Is there a module that allows you to automatically assign a sub menu for group content without the user being able to change what the menu title is called? I guess that, ideally, I'd like to have an About page that has the same title and menu path for each group.
You can try this module : http://drupal.org/project/auto_menutitle. It allows to automatically generate menu items based on the node title. If you enable this module on your og content type, it should do it.