“In the name of Jesus, whom Paul preaches, I command you to come out.”
Note they didn't claim any personal relationship with Jesus Christ--they were invoking His name as a kind of magic talisman. That was their mistake. Frankly, I know enough clergy from all denominations who are in the same boat.
Conversely, if you are truly Christ's, you already have power in His name over every demon, fallen angel, and occultic power: "And these signs shall follow them that believe; In my name shall they cast out devils; they shall speak with new tongues; they shall take up serpents; and if they drink any deadly thing, it shall not hurt them; they shall lay hands on the sick, and they shall recover" (Mk. 16:17-18). This was not an authority that the Lord gave only to "professional" clergy, but to all who trust in Him.
It is very important that a person doing a deliverance is placing none of his or her confidence in themselves, but is absolutely confident in the Lord Jesus Christ. The demons cannot overcome a Christian by force of power when the Christian stands in the Name of Jesus, but they will, if you let them, bluff and deceive you into giving up. Going in timidly is more dangerous than "overconfidence" (if indeed one could have overconfidence in the Lord).
I'm not saying that everyone is called to a deliverence ministry, any more than I would claim that everyone is called to go preach in the third world, for example. But every Christian has authority over the demonic, and we can't try to limit His callings to the "professional clergy." He calls who He wills.
That's a good rule of thumb. But the exorcists that I've heard speak (including the chief exorcist of Rome) say that demons can possess people who aren't necessarily in a state of mortal sin. It's far less common, but still possible. According to these exorcists, the biggest risk factor for demonic possession is the victim's previous involvement with the occult.
Additionally, exorcisms can become violent. It can take several grown men to hold down a possessed person.
I've seen footage of non-Catholic exorcisms where the demons have jumped into the people praying over the possessed person.
He also said where two or three are gathered together in His name, and in agreement, anything asked would be given them...apparently the mandate is not as comprehensive as many would like to believe.