You are able to outfit your companions with two weapons as well as armor and a helmet in The Outer Worlds, but a lot of these helmets look pretty ugly when playing the game. Luckily for us they don't show up in cutscenes or when we interact with the companion, but unless you actively hide it, the helmet will be shown when you are out in the world. It is however possible to hide the helmets on companions in the Outer Worlds.
In order to to this, pause the game (Esc on PC, Options on PS4 or Menu on Xbox One), then go to Settings. Go to Gameplay, and find the box where you can uncheck "Show companion helmets". Once this is unchecked, save the settings and return to the game, and none of your companions will have their helmets shown at any point in the game.