It’s what you are.
According to Wikipedia, a not-for-profit agency is an organization that uses surplus revenues to achieve its goals rather than distributing them as profit or dividends. That doesn’t sound like a description of what something is not to me. It sounds like what it is!
“Not-for-profit” is a bad way to describe what these organizations are. Nonprofits exist for a purpose. They’re pro-mission. They do all kinds of good things for society and in the world. Not for nothing, but there’s a need for some re-branding here.