You are talking about how the character is titled throught the script right? It depends on the character's importance in the script and also on dialogue.
Example 1:
DETECTIVE JOHN ADAMS greets OFFICER SCHULTZ at the door. (OFFICER SCHULTZ is a minor character)
JOHN
Hey Schultz, you got my papers?
SCHULTZ
Get them yourself.
Example 2:
DETECTIVE JOHN ADAMS greets OFFICER TONY at the door.
JOHN
Hey Tony, you got my papers?
TONY
Get them yourself.
Example 3:
DETECTIVE JOHN ADAMS greets WATCH OFFICER at the door.
JOHN
Hey, you got my papers?
WATCH OFFICER
Get them yourself.
See how the above flow together and are consistent as to not confuse the reader with extra surname/first names? Of course, in writing a fictional story you strive to avoid having characters with the same names so you avoid writing: JOHN ADAMS, JOHN DEERE, JOHN HANCOCK, etc.
I have been told by sold screenwriters that you should strive to avoid any potentially confusing or ambiguous issues in your spec script, i.e. when a producer reads it.