An excellent example of something that clearly wouldn't be distinctive since all AI related endeavors bill themselves as unicorns.

It doesn't actually mean anything though, so I think it would pass as a trademark. Apple Computer is allowed because Apple doesn't mean anything in relation to computers. You might have trouble with Mouse Computer unless you were the company that invented or popularized the mouse.

Not sure that’s an adjective

If you use it like unicorn poop, then it is describing the kind of poop just like Open/Green/Free in previous examples would be describing AI

That doesn’t mean it’s an adjective though

https://en.wikipedia.org/wiki/Noun_adjunct