In order to customize your character you'll need to craft a mirror and place it at your base. In the mirror menu you'll be able to change the nickname and gender of your character, as well as to express your individuality by choosing the colour and style of the hair and changing the complexion and beard. Remember that changes can be saved for coins, so think very well before getting a new haircut. 
Changing the look of your backpack and underwear is now possible via another structure at your base - the Wardrobe. To do that, learn the unique blueprints that can be obtained for completing different tasks, in the in-game store or as a seasonal reward.