Does a drone company hold the Part 107 or does each shooter need their own
The Part 107 certificate is held by the individual pilot who passed the knowledge test, not by the company. There is no company level certification the business registers before it can bill for aerial work, but the FAA does require the drone itself to be registered, and that registration sits with the owner or operator. Only a certificated remote pilot may act as pilot in command on a commercial flight. A shooter without the certificate at the controls is a real compliance gap unless the flight runs under the direct supervision rules Part 107 allows. A general liability policy that makes no mention of aircraft will very likely exclude drone operations. A certificate of insurance for drone work requires an endorsement or a standalone aviation liability policy written for unmanned aircraft, which is worth sourcing from a broker who writes UAS coverage before the next paid shoot.