Most people don't wreck a hat by wearing it. They wreck it in the ten minutes they spend packing it. If you want a hat to keep its crown and brim shape for years, the storage rules are short: be careful when you travel, never move it around while it is wet, and past that, wear it as hard as you want.
The fastest way to wreck a hat is travel
The easiest way people mess up a hat without realizing it is when they travel. You throw it in a suitcase or drop it at the bottom of a backpack, pile everything else on top, and over a few trips it slowly gets crushed out of shape. For a quick trip it will be fine. The damage builds up over time, so it is the frequent traveler who ends up with the warped brim.
The other big one is water. If you get the hat wet in the ocean or a pool, let it dry before you start moving it around. A wet hat is soft, and if you manipulate it too much while it is soaked, it starts losing its shape and holds whatever you bent it into. Get it dry first, then handle it.
How I actually pack hats when I travel
I usually travel with a couple of hats at a time, and the hat is the last thing I pack into my backpack. That is the whole trick. By going in last, it sits on top of everything instead of under it.
Two things I check before I close the bag. First, that there is enough room for the brim so it is not bending against the side of the pack. Second, if it is a structured cap, that nothing is pressing into the front panel hard enough to dent it. The front panel is where a structured hat holds its shape, so a hardcover book or a charger jammed against it is what leaves a crease. Give the brim space, protect the front panel, and you are more than fine.
That is honestly the entire travel routine. There is no special case or hat box involved.
Past that, just wear them
I don't want this to read like our hats are fragile, because they are the opposite. They are high quality and made to last, so besides the travel and water stuff, do whatever you want with them.
Here is the example I always come back to. We had two customers travel through Europe for forty one days. They wore the hats every single day, across at least twenty cities, and the hats came back in great shape. That is the test I trust more than any care label. They are made to wear, they don't get destroyed, and if you treat one like a hat you actually use, it holds up. You can see how the rest of the full collection is built the same way.
If your cap caved in or the brim warped
Sometimes it happens anyway. If a structured cap caves in or a brim warps, the best thing you can try is reshaping it with a little heat, and a little water if water is what caused the problem in the first place. Work it gently back toward the shape it should hold and let it set. It does not always come back perfect, but most of the time you can get it most of the way there.
A couple things I do with my own hats
Two habits that aren't obvious. When there are sweat marks, I pat the spot down with a wet rag instead of soaking the whole hat. Soaking is how you turn a small mark into a bigger problem, especially around a patch.
The second one is about drying. After you clean a hat, there is usually still some dirt and sweat left in it, and as it dries that stuff travels with the water in one direction. If you hang the hat to dry pointing down, all of it drips into the brim and leaves marks right where everyone can see them. So I set the hat flat to dry instead. Same hat, same cleaning, but the marks end up nowhere instead of across the front.
Take care of good things and they last. And if a hat does finally reach the end of its life after years of real use, that is what the newest drops are for. We keep releasing new ones, so there is always a different style waiting.