So long as you have a companion currently in your party, their equipped gear will appear when you cycle to them. This opens the inventory menu where you can click either arrow next to your name at the top, center of the screen, to cycle characters.
This is similar to changing your own gear when you go to your inventory by pressing 'I' by default.
The first step to fully customizing your companion is upgrading their armor and weapons. How to Change Companion Armor and Weapons How to Increase Your Companion Party Limit