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.
If I may piggyback on your answer, Salpy:
I have heard and read the same thing (which really doesn't prove or disprove anything). In light of the argument that Fr. Arseny wasn't a real priest, or that Arseny wasn't his real name (I personally believe he is real and that his Ekklesiastical name was Arseny), it might help to view the book in the same vein as "The Way of a Pilgrim". We don't know who the Pilgrim was, or even if
he was. But the spiritual insights provided in the book are amazing and beneficial for us to read.