Counting as underarmor, the matching hood for the Brotherhood of Steel uniform is typically worn under power armor (like Paladin Danse does). It features numerous ports seemingly designed to interface with the wearer's power armor,[Non-game 1] though it is not required to wear one and does not provide any additional functionality when worn underneath a suit of power armor.
Worn by Paladin Danse and can be traded once he's been recruited as a companion.
Behind the scenes
The BoS hood is functionally equivalent and visually similar to Communications Carrier Assemblies used in several NASA spacesuit models, commonly referred to as "Snoopy caps."
In the opening cinematic, a helmetless soldier in power armor is seen wearing a similar hood, suggesting that they were standard issue during the war and later adopted by the Brotherhood.
The hoods are also similar to the headpieces for recon armor seen in previous games as those are also based on undersuits for power armor. However, unlike previous games, it offers little protection.
↑Fallout: The Roleplaying Game Rulebook p.125: "The matching headpiece for the Brotherhood of Steel uniform, this close-fitting hood was developed before the Great War for wearers of Power Armor. It is designed to plug into the helmet of a suit of Power Armor, providing a closer interface to the armor’s systems, as well as containing an earpiece and micro�phone for the armor’s internal radio."