But "hymns" only really refers to a limited range of sacred music -doesn't include Gregorian Chant for example, or Christmas Carols, or canticles, or lots of other varieties which from your opening post you'd want to be open to. I mean, you wouldn't call Lord of the Dance a hymn - at least Sydney Carter never did.

That's why you get collections with titles like "Songs of Praise", "Worship Songs", or "Sacred Songs and Solos" (Moody and Sankey that last, more than a hundred years ago).

That doesn't help with coming up with a name - most names I've come up with so far, when I checked them, they are already used.   Even "Amen" is the name of a battered men's support group in Ireland.

Holy Music seems to be unused for anything of this sort so far. It's got the merit of being a pretty intuitive name, and very inclusive.