The Center for Nonviolent Communication (CNVC) holds trademarks on the terms Nonviolent Communication, NVC, Compassionate Communication, and a number of other terms. CNVC also certifies trainers who teach NVC. One need not be certified in order to teach the ideas offered by NVC, but there are a few requests that CNVC has for non-certified individuals who share NVC, including not using "Nonviolent Communicaiton" in the title of trainings that they offer, and crediting CNVC.
Aside from these sorts of limited centralized administrative factors, practitioners and teachers of Nonviolent Communication form a movement, not a particular organization. They may be associated with one or more NVC organizations, often with a regional focus, which promote NVC in informal alliance with CNVC but without any formal relationship. Most NVC trainings are offered by independent trainers, or by trainers acting in association with one of the many NVC organizations.