Axanar uses the name of one character seen in a single episode of the original series.
True, but that's not all they use. They use the races and names of Federation members and enemies...Vulcans, Klingons, etc.
Despite that, I think CBS and Paramount are being jerks with this and need to back off or come to a mutually-acceptable agreement with the Axanar crew. I, for one, want to see this film made. I would watch it in a New York minute. (If you doubt me, look up the short film "Prelude to Axanar" on YouTube. If the production values are any indication, this film will be excellent.)
And thats what they did which got them in trouble. I get it.
With Twilight fanfiction that went to publish, all names were changed which got those authors free from legal entanglements over copyright infringement.