Gaiter or buff

Buff is a brand name that became the general word. The tube covers the neck, and pulled up it covers the lower face and ears, which are the places a hat brim misses and where skin cancers most commonly show up on people who spend their lives outside.

It doubles as wind protection in cold weather and, wetted and worn damp, as evaporative cooling in heat.

A hooded sun shirt with a built-in face mask does the same job with nothing extra to lose, and that design has largely taken over.

Breathing through one is the common complaint. Thinner, more open knits are easier to wear over the nose for hours, and some designs add a mesh panel over the mouth for exactly that reason.

Check the UPF rating on a gaiter as well. A cheap polyester tube with no rating gives you far less protection than the number of layers suggests.