The name is Albrecht Dieterich's. Publishing the passage in 1903, he identified it as a surviving initiation text of the mysteries of Mithras, which would have made it the only ritual script from a mystery cult otherwise known almost entirely from its archaeology and its images. That claim is the reason the passage is famous, and it was contested immediately.
Franz Cumont, whose reconstruction of Mithraism dominated the subject for a generation, held that the identification failed on the evidence. The Mithraea are full of a recognisable iconographic programme, the bull-slaying, the torchbearers, the grades, and almost none of it appears in the text. What the text does contain, Egyptian divine names and the technical vocabulary of the magical papyri, appears nowhere in Mithraic archaeology. The passage, on that reading, is Graeco-Egyptian material that happens to use a fashionable Persian name.
The atlas records the identification as debated because both positions are live and have serious holders. Dieterich's side points to the Mithraic name itself, to the solar imagery and to the seven-stage structure. Cumont's side points to the total absence of corroboration from the cult sites. Hans Dieter Betz's 2003 commentary, which is the standard modern treatment, occupies a middle position: the composition is Graeco-Egyptian, but the borrowing of the name is not accidental and tells us something about how a Mithraic reputation circulated. The label is now used as a convenience, and most scholars who use it say so.