Hello Romane,
In your example,
Company XYZ (in EU) will be Specification Developer;
Contract Manufacturer (in US) will be Contract Manufacturer.
Both these entities have to list their Establishment with the FDA. Once the establishments are registered , the Device Listing has to be completed where the CM must tag their device with the Company XYZ's device listing. Remember the facilities are "registered", while the devices are "listed".
Now, when you say "Importer", I am not clear what you mean. The CMO has to "export" to EU, correct?