This is a little arcane for us and I am unfamiliar with this incident but remember that demons are simply fallen angels, with the same classifications. So there are also thrones, cherubim, seraphim, and others among the demons.
As for Gregory, the reference I found for this was in Wikipedia:
It referred to a chapter, "Asmodeus, dandy among demons", in the book,
I found what certainly appears to be a copy of this chapter:
— [PDF] Asmodeus Dandy Among Demons.
online, and found no such reference. The book Evil Archaeology: Demons, Possessions, and Sinister Relics by Heather Lynn does mention it, but without attribution. I can find no primary source for this either on the Internet or in my extensive offline resources.
Supposing that it is true. I would submit that what Pope Gregory did was simply identify him as a throne, not appoint him as a throne. No angel could be appointed by a pope as a particular classification. That would be as absurd as saying that the pope could appoint a dog to be a human being. He simply has no such power.