Having looked at all these versions, an observation here (in case anyone else is as slow as I was to figure this out it): We are probably punctuating this wrong. Take Joe's first verse. It should probably be:

The ring on my finger is.
Johnny give me.
The ring on my finger is.
Johnny give me.
The ring on my finger is.
Johnny give me.
Johnny alone until morning.

That is, the verses should be understood as "The ring is on my finger. Johnny gave it to me." Not "The ring on my finger is [called] 'Johnny give me.'"

According to a quick Google search, Nevis Creole has a tendency to reorder words in a way atypical of English. In this case, it appears they're using subject-object-verb word order rather than the usual English subject-verb-object.