Any western hat will keep its shape and look good for years if you store it properly.
Keep the front, back and underside of your cowboy hat from resting on a surface any way you can.One way is to roll a large towel or sweatshirt into a ball. Stuff this inside the hat leaving enough underneath that the hat sits all the way up off the shelf. This keeps the pressure off the brim and will keep the hat brim from flattening out.
You can use your cowboy boots as a hat holder.
Or if your hat has a firm crown, you can turn it upside down and store it on its top.
But NEVER leave your cowboy hat on the dashboard of your truck. The heat and humidity can cause irreparable damage.