And you think he changes his emblem every time his orders come from a different authority? I don't know about the plausibility of that, though I could imagine the assignment patch being an update-able display, like e-ink or something.
Hmm...I like that. Since Scotty obviously starts to show interest in female biology in "The Lights of Zetar" his department accordingly changes from "engineering" to "science" ...
(Seriously, maybe it was an inside joke of the producers)
KIRK: Scotty, where've you been? Where are you?
SCOTT: In the Sickbay.
KIRK: Are you sick?
SCOTT: Och, no. I was just checking on the lass. She's going to be fine now. There's nothing wrong with her.
KIRK: Well, I'm relieved to hear your prognosis, Mister Scott. Is the doctor there with you, or will I find him in Engineering?