Just before leaving the starting area, I got a "Vette Customization 2" as one of the quest rewards. Right-clicking it just tells me I can't equip it.
How do I apply it to Vette?
You have to have your companion open on the character sheet and then you can right click on the customization. This also applies to any companion named gear that you might receive as quest rewards and is how you equip all items onto your companion.