Single registration number is a number that each business entity has to get from the EUDAMED or local competent authority. A single registration number has to be asked for a manufacturer, importer, and EU representative. Distributors do not need to be registered in the EUDAMED. It is covered in Article 31 of the MDR 2017/745.
Considering the codes, there are specified codes for medical devices. MDR has a code that is called European medical device nomenclature covered in Article 26 of the MDR. More details regarding this nomenclature you can find on the following links: