Just be sure to keep track of the default groups. The destination group for new users is hard coded as user_group_id 2. Changing the group name is a superficial change.
When people want to change the destination group for new users I always advise them to simply treat the Registered group as if it were the new group. Set appropriate permissions for Registered just as you would the new group.
FYI, the default groups are hard coded into this file:
public static $defaultGuestGroupId = 1;
public static $defaultRegisteredGroupId = 2;
public static $defaultAdminGroupId = 3;
public static $defaultModeratorGroupId = 4;