After half an hour or so with Google, I finally found a manufacturer's web site which admitted that the new bamboo fiber that is all the rage now is "regenerated" -- so add "bamboo" to the list of rayons.
Unfortunately, I was so chuffed to find the datum that I forgot to notice the manufacturer's name or save the URL.
For further research: are the old-time protein fibers made from corn and soybeans regenerated or synthetic? And a philosophical question: should there be a new category, "concocted", for fiberglass, which is man-made, but neither regenerated nor synthetic.
"Concocted" might also fit the vegetable-protein manmades; certainly there are no protein fibers in seeds, so "regenerated" wouldn't fit very well. I don't remember enough about them to feed keywords into Google, I might get find their names by reading related articles in Wikipedia, and one of them was marketed as "soysilk" a few years ago.
Joy Beeson