that is not a hat. that is a cover
A cover is military nomenclature for headgear, what many call a hat, or cap. If I put on my dress uniform and go outside, I wear my cover. My cover comes off when I enter a building. That, however, is not a military piece of headgear, therefor it is completely okay to refer to it as a hat or a cap. If you refer to it as a cover, you are not wrong, but if you refer to military (at least USMC) uniform headgear as a hat, you are.
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