The original manufacturer of Eastwood's hat is not known. This knowledge seems lost to time since both the director and the film's costumer have both passed away. It may have been purchased by Eastwood in Los Angeles and brought with him to Spain. What seems apparent however is that the hatband that was seen in the films is probably not the original hatband that came with the hat.
The original hat? Yeah I know who made it. He's passed away now though. I have his name written down around here somewhere. I'll look for it. - Don Livingston, Longhorn Hatters
Loose threads can be seen in the high resolution Blu-ray copies of the film that held the hatband to the hat but are torn loose on the front of the hat and on Eastwood's left side. The right side of the hat appears to be sewn to the hat. The front and right side of the hatband each have two tiny holes through the leather for the thread to feed through.
The hatband might possibly have been made by Andy Anderson who made the holsters and other leather pieces for the films. This is unconfirmed however.
The hat is the most beat up and weathered in appearance in the the third film despite it being chronologically the first chapter in the trilogy.
The hat is given to Blondie by Angel Eyes (in addition to his railroad stripe shirt) as "new" clothing at the POW camp. Angel Eyes theoretically may have sourced the hat and shirt for Blondie from a captured Confederate civilian soldier or they may have been taken from a Union civilian soldier. Or salvaged from a dead body which would possibly explain the pre-existing bullet holes.
His hatband's buckle switches from Eastwood's left to his right a few times in the films. The shots may have been reversed, or the band was accidentally rotated.
His hat starts with bullet holes already in it and has an additional 6 shots fired through it by Mortimer (which strangely go completely unseen in later scenes).
The hat's material is thin enough that it can fold up in the wind.
The hatband looks to have been a replacement for the hatband that originally adorned the hat. Torn threads that attached the hatband to the hat can be seen loosely hanging from the hat in high resolution stills from the films.
It's theorized that the hatband was provided by Andy Anderson who provided Eastwood with his holster.
That was a fairly standard simple carving pattern for a narrow hatband, they could well have both been made in Andy Anderson’s workshop, I wouldn’t know for sure but it’s more than likely. I do know that Andy made stuff for Bronson as I have an AA gunbelt which he made for him. Bronson went to Europe to film and didn’t collect it, I’ve had it for about 40 years. - John Skelton, Escort Gunleather
Screengrabs of the hat and hatband from the trilogy of films.