Albert Barnes Commentary Mark 1:34

"And he healed many that were sick with divers diseases, and cast out many demons; and he suffered not the demons to speak, because they knew him." — Mark 1:34 (ASV)

And suffered not the devils to speak, because they knew him. They knew that he was the Messiah. If they had spoken, they would have made that known to the people. Jesus did not wish, at that time, for that to be publicly known, or for his name to be widely proclaimed. The time had not yet come when he wished it to be proclaimed, and he therefore imposed silence on the evil spirits.