As with his healings, Jesus commands the demons to leave without invoking an authority (Matt 8:28-34). Later exorcisms in Acts are done in the name of Jesus, but Jesus simply command the demons and they leave the victim. In fact, knowing the name of the demon was consider the first step in an exorcism. In Luke 7:26-36 Jesus encounters a man with a demon living among the tombs near Gerasenes. This demon speaks to Jesus and calls him “Son of the Most High God.” This ought to have given the demon power of Jesus since he knows Jesus’ true name. But Jesus simply commands the demon to give his name, then commands the demon to come out of the man. No other authority is necessary for Jesus to cast out the demon, they simply obey him.
Also absent from Jesus’ exorcisms are the elaborate preparations for an exorcism described in contemporary literature. [Tobias] took the live ashes of incense and put the heart and liver of the fish upon them and made a smoke. And when the demon smelled the odor he fled to the remotest parts of Egypt, and the angel bound him (Tobit 8:2-3). The Testament of Solomon is more or less a manual on how to cast out demons written in the third century A.D., although it may contain material from much earlier. In this story, workers in the Temple find a ring which is able to control demons. Solomon then captures and interrogates a series of demons. They are forced to give there name and what they are in charge of as demons. Then Solomon forces them to explain how they are cast out. For example, in chapter16 Solomon interrogates a demon called Kunopegos, a spirit in the shape of a horse in front and a fish in back (a sea-horse?) He can change himself into a man and causes seasickness. In order to thwart this demon, one must go through a complicated ritual involving bowls and hemp ropes. Solomon sealed him with his ring and stored the demon away.
What is the point of Jesus’ exorcism ministry? Twelftree argues that there is a two-stage defeat of Satan being described in the gospels, the first mission of Messiah render the power of Satan useless, it is in his second coming that he will judge him and consign him to the Lake of Fire (270). Satan is trying to hinder Jesus’ ministry, but Jesus constantly defeats him with no struggle whatsoever.
G. H. Twelftree, “Demons, Devil, Satan,” in DJG 163-172.
Wendy Cotter, Miracles in Greco-Roman Antiquity: A Sourcebook for the study of New Testament Miracle Stories (Routledge, 1999).