Many people are uncomfortable with the "non" part of Nonviolent Communication. Note that the "non" is really part of the word nonviolent, the history of which, going back to Gandhi's use of the term ahimsa and earlier, is non-dual. That is, it's not just about not doing harm, but about having genuine compassion even for those you are in some sense working "against." Specifically, being against violence in some harsh or moralistic way is not nonviolent. The goal is to transcend, and organize for change without judging those who are being violent.
Anyway, there are a number of other terms people have come up with for NVC. Compassionate Communication is very commonly used, including by the Center for Nonviolent Communication. When I share NVC I often use the term Open-Hearted Communication (and even better, in Tamil, in place of the word for heart have used a word that means both heart & mind).