In Monster Hunter World you unlock the option to change armor color / pigments during 6-star assignments. After unlocking 6-star assignments on the quest board you must play the next main quest to slay a Pukei-Pukei and then the color change becomes available. At the same time, you will gain access to high-rank armor at the smithy in Astera. When this happens you will also receive a short notice/tutorial about changing armor pigments.
This is relatively late into the game so beware you must make a lot of progress for this to work.
Once you have high-rank armor unlocked simply go into your room in Astera and interact with the item box. Pick the option “Change Appearance” > “Change Armor Pigment”. Now you can freely pick a color of your choosing. You can color individual gear pieces or color them all at once.
Important: You can only change the color of high-rank armor (6 stars+)! Low-Rank armor cannot be colored. The only place to make the change is in the item box inside your room, it doesn’t work from other item boxes.