I think it is considered a collection of true stories coming out of the gulags. Whether Fr. Arseny really existed, however, has been a matter of debate. His character may have been invented to pull the stories together, or he may be a composite of a few different priests who really existed. Since the book was written and circulated underground while the Soviet Union was still in existence, the real names of the people involved in the stories would not have been used. That would include the priest or priests involved in the stories.