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.
Puritan exorcism
The term Protestant dispossession is also used, which allows for the differences from Catholic practice. There are a number of well-documented cases. John Darrell had a career as an exorcist spanning about 15 years; other were Robert Balsom, John Foxe, Edward Nyndge, and Richard Rothwell.