That seems fair enough to me. Are there other ships they could have used? Sure, but even without a heritage connection to the name, I do see the appeal in using one that starts with a big 'E'.
I've got no issue with using the Exeter as long as they don't use anything that was created original by the Johnsons for 'Starship Exeter' which, as far as I can tell, they haven't. Someone looked at the Exeter, a canon ship from a TOS episode and decided to tell the stories of what happens after. Someone else looked at it and has decided to tell stories about what happened long before. As long as we're all playing in somebody else's sandbox, I don't think their can be any sort of monopoly claimed on established canon property, no matter who was first and how long. Anybody who makes a fan film instead of an original production is using somebody else's creativity to inspire their own. I, personally, don't want to hinder that just because somebody else used something first.
As for the name, if they really wanted to confuse people, they could have gone with "Star Trek: Exeter" since it's technically different from "Starship Exeter" but close enough to pass. Even if I don't give them the benefit of the doubt and assume they did watch an episode of Exeter and decided to their own version of that, I'm kind of intrigued about the idea of a fan film of a fan film.
In a world where someone decided to do a show that continues the original Enterprise and crew even though somebody else had been doing that exact show for a decade, telling two distinct eras of the same ship isn't a big deal to me. This is just my opinion on it, of course, and I didn't intend to go on for this long...
