At this time there is no requirement from TSA stating operators must issue a specific ID badge to employees. These are regional requirements by airports and Fixed Base Operators. However,in its 2017 "Security Guidelines for General Aviation Airports and Users," TSA does mention airports may want to look into card identification systems for employees.
Presently NATA, NBAA and other associations have published best practices for business aviation. Among the best practices, it is highly recommended that all employees be issued and clearly display ID badges at all times when at the airport. This is for the security of both employees and society as a whole. Too often there have been incidents of people impersonating officials, employees or aircraft owners to gain access to secure areas.