Insofar as "correct" has meaning in the context of tune name conventions, I think you're right, Jean.

Incidentally (and off topic) do you have a list of your contributions to Worship in Song: A Friends' Hymnal? I've noticed (but not noted, alas) discrepancies between the index and the notes at the songs themselves. As a hymnologist and a hymnal editor, such discrepancies tend to give me pause, if not sleepless nights. I'm so glad they included your Garden hymn ("Now Is the Cool of the Day").

Haruo