A considerable component is informing end-users of the changes in this process. They will have more self-control but also more responsibilities. In some cases we have traded in the extended support and customizability of our on-site or custom services for quicker turn-around times, high-speed feature release cycles and/or cost savings.
The main governance concern for this process is alignment. When selecting a cloud provider support routes should be taken into account and adhere to the requirements of the business (or be otherwise explicitly agreed to).
(Larger) Providers of (Enterprise-like) Cloud services offer support packages in different flavors. Understanding which option goes with a specific application is something the CCoE can help with. However, contracting or activating the correct support level is not per se the responsibility of the CCoE and should therefore be the subject of discussion and implementation.
NOTE: The CCoE should not be part of the support-line or participate in incident reponse.