The term "Demonologist" can mean different things.
Consider there is a big difference between those who conjure demons, and those who seek to remove them.
A historian, or a "scholar" on the topic. This person has studied Demonology through seminary schools, has a vast understanding of demons and spiritual warfare, and is the most educated in the profession.
One who has primarily learned from the Bible as their source of information on Demons - This knowledge applies more towards Spiritual warfare. A majority share a belief that "all ghosts are demons", which is Scripturally based, and that what the world considers a ghost is no more than residual energy or imprint left behind by someone who has passed. Many Biblical Demonologists also consider themselves an Exorcist and believe the Biblical belief that any follower of Christ is capable of deliverance as it says in Scripture:
(Mark 16:17) And these signs will accompany those who believe: In my name they will drive out demons; they will speak in new tongues.
But those who are not anointed for this calling can get themselves into a lot of trouble. All we have to do is look to Scripture to verify that.
(Acts 19:13-16) Then some of the traveling Jewish exorcists also attempted to call the name of the Lord Jesus over those who had evil spirits, saying, "I implore you and solemnly command you by the Jesus whom Paul preaches!" Seven sons of one named Sceva, a Jewish chief priest, were doing this. But the evil spirit retorted, " I know and recognize and acknowledge Jesus, and I know about Paul, but as for you, who are you?" Then the man, in whom was the evil spirit, leaped on them and subdued all of them and overpowered them, so that they ran out of that house in terror, stripped naked and wounded.
Well as you know, this is one who conjures demons to do their own bidding, the black arts practitioners, etc.. This is the most common definition for "demonologist" prior to the introduction of the title "demonologist" into the mainstream before 1990.
KABBALA AND MYSTIC DEMONOLOGISTS
Be especially aware of people teaching this material in their "Demonology course"! These are "demonologists" who consider the Gnostic text "The Keys of Solomon" as legit, expecting it to work in spiritual warfare, although they are calling upon demons to do battle against demons. Anything with the likes of "Aleister Crowley" or "Goetia" is to be avoid. There is a certain level of ignorance in people learning Demonology from the perspective of the enemy. Yet they believe it applies to Exorcism and Deliverance. Wrong!
"A house divided against itself cannot stand,"" -Matthew 12:25
"How can Satan drive out Satan?" Matthew 12:25-referring to exorcism
This is the most common and exploited title people assume applies to a demonologist. This specific one is the title Gerald Brittle created to describe the unique work that the late Ed Warren did for his book "The Demonologist". However, during that time this was simply another title for a Catholic demonologist that is now used by people with a lack of knowledge of its true origins and believe that this title applies to all Christian demonologists. Now, there is little to no qualifications to use the title, which means it's inconsistent with the people who use this title. You could go from somebody who has education in this field, to someone who has no knowledge at all in the field.
Specific to a particular faith or organized and known denomination working directly through their church and coming from a perspective related to that faith/denomination. This individual may or may not also practice what is considered "Religious Demonology" or merely be an adviser for demonology and such related information, or it may be an embodiment of all types of demonology listed here.
Roman Catholic Demonologist
Although they might handle cases abroad, the prefix dictates they are under the authority of the church doctrine of their Roman Catholic church and magistrate. It is assumed by default such individuals are somehow recognized by their local diocese or in the least their own parish church, although it may not be publicly. However, due to Catholic beliefs, permission must be granted through proper channels in order to perform any deliverance, which means this is possibly the longest way of getting help for your circumstances. There is usually a long documentation process. Sometimes this can take a month to several years for the church to give approval for your circumstances.
Through their own church they might be a member of a deliverance team or prayer group that works with such cases of infestation or possession. They are more or less focused on spiritual warfare and have little to no understanding of demonology itself, but they are capable in some cases in providing assistance.