What do you call the kind of sling swivel that the loop that holds the sling can rotate independent of the wood screw and where can I them?

Try Uncle Mike's brand!

Can get them any where!

Midway USA!

For starters

uncle mikes doesn't make a swivel like that. Don't think you under stand what I'm asking about

Grovtec makes a number of styles. Are these the ones you are looking for? https://grovtec.com/collections/swivels/products/standard-push-button-swivel

I don't think I have ever seen a swivel that worked like that unless. it wasn't installed right. It might swivel like that,
If you had a sling that swiveled, the the sling would twist also.
I have used the Grove Tech swivels-----only on request! A pain in the ass to install and nobody wanted to pay for the extra labor.