Making up a new name really? I have an open source project that I am thinking about monetizing. In the end as an author you actually have to choose a sensible license set-up for that project.

If this then counts as open-source or not really only matters for marketing purposes. And a new term will not have the same effect for that. If I put fair-source on my landing page it just means I have to explain more.

People that really care about the license will read the license. People that don't really care will be fine with generic terms imo and don't need the classification.