The person whose name appears on the registration doesn’t have to hold a remote pilot certificate, but the person flying the drone does have to have proof of registration in their possession while flying.
There are a couple of ways you could go about registration.
1) This option is the fastest and costs $5 per drone
You could register the drone online via the FAADroneZone under the person in charge of the drone program or the primary pilot-in-command. The draw back to this option is that if/when this person moves to a different position. The drone will once again have to be registered for commercial use under the new person’s name.
2) This option could take 2-3 weeks to process, but the cost is still $5 per drone. You could do a paper registration and register the drone to the ‘company’ instead of an actual person.
This second option eliminates the need to re-register the drone to a different person in the event the person changes positions or leave the company.
You’ll need to complete the Aircraft Registration Application, AC Form 8050-1 and have a notarized affidavit verifying ownership. But in the long term, this could be a better option.
More information on that process over here:
https://www.faa.gov/licenses_certificates/aircraft_certification/aircraft_registry/UA/