Guessing you mean that you attend a parish where the Extraordinary Form is celebrated by the Institute of Christ the King. They are small in the US, having only 2 superiors in our country.
ICK is Apostolates and Provences who operate in with the permission of the Local Ordinary, however, like religious orders, they do some things differently. Choosing to publicize the names of their exorcists is at the discretion of the Institute’s Superiors/Bishop.
I am speaking of Secular priests. The Bishops of the United States rarely publicize the name of the exorcist, one needs to first speak to their parish priest instead of “self diagnosing” any sort of possession. Sort of the way that you need to see your GP doc to get a referral to a surgeon or other specialist.
If this young man is seeking to inter the Institute, their process is different than that of a Diocesan priest. From my second hand experience (friends who have discerned vocations in the ICK), their process is rigorous. Our OP would want to begin attending Mass with the ICK and speak to his pastor there about discernment http://www.institute-christ-king.org/vocations