In the tie-in novel Dale Cooper My Life And Tapes, Diane is identified as Dale Cooper's PA and secretary
Best explanation is that Diane is Cooper's secretary at the FBI. Every time he fills a whole tape he mails it to her and she transcribes it, takes notes, etc. We see him greet her in the office in the movie (FWWM) but even then we don't actually see her. It should also be taken into consideration that when Cooper asks Diane for earplugs, he receives them almost instantly.
The fact that Cooper does receive the earplugs almost instantly, though, is also strange. Cooper mentions the fact that he needs the earplugs on the tape but is never seen phoning Diane to ask her to send them. This would then presume that Diane knows he needs them via the tape. That then means that Cooper has to mail the tape to Diane, Diane has to listen to the tape, then procure the ear plugs, then send them back to Cooper in Twin Peaks. This entire thing took place in a day during the story, which is almost impossible. It is almost as if when Cooper records a message for Diane on the recorder, she gets the information instantaneously and possesses some kind of ability to materialize his needs for him.