Rok, at first I was confused by your post.
****I feel you and The Frogman might be putting too much emphasis on the name of the tune. I don't think of Vermont at all.****
Huh!? The tune IS about Vermont. You can't remove the lyrics from the equation. A great song is a marriage of melody and lyrics, and the message can be sent by the lyrics, the tune, or both. In Moolight In Vermont, while I don't know what Vermont is supposed to sound like, I think the tune, by itself, conveys a feeling that is similar to (and definitely compliments) the lyrics. It's a beautiful song, and interestingly, has no rhymes.
****You gotta name it something. Something people can easily remember and relate to.****
The name usually relates to the lyrics. Usually, a composer is inspired by an event, person, or place to convey the feeling in song, and the name is part of the lyrics. You may find this interesting, with Herbie Hancock speaking about the creation and naming of his tune "Watermelon Man":
http://bluespianorevealed.com/herbie-hancock-and-the-origin-of-the-watermelon-man/