帽垂布(Boutare nuno)
I protect a neck from strong sunlight.
It has a long history, and it was attached to the junkasa of the lower infantry during the Warring States period.
I have a few adult sized hats like you have there in the second link like a baseball cap with material hanging off the back. I bought them when i was in Japan as you may suspect for the reason of not burning the back of my neck so bad when out. I have not looked for them in the US yet.