I looked through Netlify and Vercel pricing, and their open source team option forces you to put a badge in your site footer, if you get accepted in the open source plans. The only service that doesn’t seem to require that is Render: https://render-web.onrender.com. Have people heard of any other services for static sites (which offer preview deployments)?
You really don’t want to just put a name in your footer?!
Vercel is amazing. Just try that.
Alternative: GitHub pages
I use Vercel every day. I don’t think I can get the footer change approved by directors of one website.
I didn’t see a way to do pr previews quickly with github pages.