You might be interested in fair.io, launching next month. We ran into a similar problem a year ago that ended up stirring up a lot of drama, so we are now promoting the term Fair Source instead of Open Source.
I wish you well but the name is unintuitive (Why fair? Is there an unfair source?) and the definition¹ is vague.
1. Fair Source is software that is safe for companies to share and developers to use. It's best for a company's core products, not shared infrastructure.
Creating a new term to describe this licening model may be a good idea... but it appears that that the linked website has no definition for what the term is supposed to mean yet? Is that something you intend to remedy in the future as a definition is decided upon?
I would also echo other commentators that the name may lead to a belief that you are implying that other software models aren't fair. If that is not your intent, then adding an explanation of it on the website may be a good idea, so that others will know why the name "fair" was chosen and how it is meant to be interpreted in relation to the other licensing models.
I agree that we need a new term for licenses that are between traditional "source available" where the source code is published, but the license restricts any real usage, and fully open source.
However, I don't like the name "fair source". It implies that open source is somehow unfair, which I don't think is fair.
I see where the name comes from, since it is trying to be more "fair" to the creating company by preventing another company from building a product without putting any work or money into it. But compressing that nuance into the word "fair" is IMO potentially confusing.
