Exorcism
In Catholic Christianity, exorcisms are performed in the name of Jesus Christ. A distinction is made between a formal exorcism, which can only be conducted by a priest during a baptism or with the permission of a bishop, and "prayers of deliverance" which can be said by anyone.
The Catholic rite for a formal exorcism, called a "Major Exorcism", is given in Section 11 of the Rituale Romanum. The Ritual lists guidelines for conducting an exorcism, and for determining when a formal exorcism is required. Priests are instructed to carefully determine that the nature of the affliction is not actually a psychological or physical illness before proceeding.
The Exorcist
In "Angel: Earthly Possessions", a spin-off comic story based on the TV series "Angel", protagonist Angel finds himself dealing with a priest who performs exorcisms, but comes to realize that the priest is summoning the demons for him to exorcise in the first place. He also makes a note of "The Exorcist" film, noting that the vision it created of possession actually made things easier for possession demons by making it harder for humans to know what to expect from a possession.