I had fun searching for this song. It's amazing how many songs contain the phrase "everybody knew my name." Many of them are about the fleeting or unsatisfactory nature of fame: "I was a rock star, everybody knew my name, but…" Some of them are rock songs or even rap. I ignored those. I will post the ones that seem kind of folksy. But so far, I haven't even looked for variations like "everybody knows your name" etc. The one that seems most like the theme you had in mind is the following one, although it isn't exactly a folk song, either. I found it quoted in a sermon, of all things, so I don't know if the lyrics are complete.

MIRA
(Bob Merrill)

I came from the town of Mira, beyond the bridges of Saint Claire.
I guess you've never heard of Mira. It's very small, but still it's there.
They have the very greenest trees and skies as bright as flame.
But what I liked the best in Mira, is ev'rybody knew my name.
Can you imagine that? Can you imagine that?
Ev'rybody knew my name.

[Originally sung by Anna Maria Alberghetti in the role of Lili in the musical play, "Carnival," 1961.]