To update an tag group, pass the name as a parameter and the ID of the tag group is passed as part of the URL.
URL Query Parameters
tag_groups_name - The new name of the tag group
user_define - 1 or 0 - Set to show on product add/edit page as editable field
user_select - 1 or 0 - Set to show on product add/edit page as a drop down list
search_filter - Show as a search filter on category pages