No, of course not. A tm or ® indicate something is being used as a trademark with proprietary rights on the brand with respect to particular goods or services. Your driver's license or SS card are not "goods or services". You cannot, under any circumstances, use trademark laws to prevent anyone from using your personal name or business name as a reference to you or your business. .
If your name were "WALT DISNEY", you certainly would not put ® on it anywhere when referring to yourself, although you might use the tm or ® for the identical name on your goods or services.
Mis-use of ® is a violation of federal regulations, not that anyone cares.