Monsignor Pope Ping!
My pastor talked about this episode during daily Mass recently. He said that a commentary he read mentioned that claiming, "I know who you are!" was culturally recognized as an assertion of spiritual power. For one person to tell another, "I know who you are, (your name here)," was to claim spiritual control.
So in these incidents, the demons are attempting to assert spiritual power over Jesus. That's why, "He would not permit the demons to speak, because they knew Him." We also see this concept in some interactions with other people, such as those who ask, "Is this not the carpenter's son? Is not his mother named Mary? We know where this man is from!" People don't like it when someone breaks out of the constraints that have been put on him."
It reminded me of a song, "You're Always 17 in Your Hometown," by Cross Canadian Ragweed.
https://www.youtube.com/watch?v=nR6pkU-_MK4