The "specialitetsnummer" is the "ID" number attributed by the authorities responsible for drug registration. When a pharmaceutical company applies for the authotisation to market a product in Denmark, this product is then by the Ministry of Health's dept. for drug registration regarded as a "ny dansk specialitet", a new Danish drug product, where the novelty aspects lies in the fact the product is being introduced for the first time on DANISH markets (even if it is not new as such). It is then attributed a "specialitetsnummer" and listed on the Drug Registry listings.


Since the number is attributed by the authorities responsible for registering the drug, I would put emphasis on Registration so the translation would be: "Drug Registration number"
See for instance § 7 in the Danish Law text reference below.

Excerpt from the law text recommende below:
"Ved en ny farmaceutisk specialitet forstås et lægemiddel, der ved udstedelsen af markedsgøringstilladelsen tildeles et nyt dansk specialitetsnummer."

translation:
"upon giving a new therapeutic product the "markedføringstilladelsen" (NB: funny enough there's a spelling mistake in the law text)[meaning the authorisation to market], a new Danish specialty number is attributed."