When I worked at another airline many many moons ago. Came in for a 4 am shift, my desk was barely up and running let alone me. Phone rings, I answer and immediately say in a straight tone, "You have reached XXX Dispatch. We are currently closed. Please call back during normal dispatch hours. If you need to leave a message, press 1.... Then I heard in the background, Hey I didn't realize dispatch closed, when do they open.
Now I had to change modes and get this persons attention. Explain what was going on and that yes we were present.
At least said person had a sense of humor, otherwise......