You are very right. Actually no engraving or anything was allowed on any gun registered on your card. some guys snuck them on after the gun was inspected at the armory. Many guys had them put on their Los Angeles Police Dept model 68s. In the armory we kinda looked the other way.
I tell you this "Policeman" Badge #1208 would have been issued a loooong time ago. Went to Police Officer in 1974 , I believe. Pete Malloy's badge Policeman #7-- would have been an early 60s 2-3 maybe. His partner a rookie in 68 was 24--. I think they tried to keep thing current on the show. The badges were actual LAPD badges , I was told and neither guy got their actual badge when the show ended. Only Jack Webb was so honored. Or so the story is told.
Neat on your gun, and a lot of guys did that to their guns after they retired, which is cool.