A name tag was a sign worn by an individual that gave their name and sometimes their occupation or title.
In 1986, employees of Mercy Hospital wore name tags. Police officers stationed outside Pavel Chekov's operating room also wore them.
(Star Trek IV: The Voyage Home)
In the 22nd century, Starfleet personnel and MACOs had their names affixed to their uniforms. (Star Trek: Enterprise)
In 2371, Kathryn Janeway identified Amelia Earhart by the name tag she was wearing, which read "A. Earhart". (VOY: "The 37's")
In 2373, Garak lamented the name tag he was given at a Bajoran conference on the Occupation of Bajor, which read, "Elim Garak, former Cardassian oppressor". Jadzia Dax questioned whether he would have preferred it to read "former spy" instead. (DS9: "Things Past")