While the character creation in Biomutant will have an interesting effect on how your character looks, this is not set in stone. All manner of things will impact the overall appearance of your character, such as the breed and stats you pick, but you don’t have to look that way forever.
To do this, you will need to find a character called Trim who is located to the southeast of Suburbia. Suburbia can be found almost directly south of the Tree. If you speak with Trim at his stall, he will give you a mission called “Lost Not Found” where you will need to buy a special item from a character called Juju. This item, the Barber Clipperfingers, can be gotten from Juju if you simply head to the area marked by the waypoint when you pick this mission in the journal.
Purchase the Clipperfingers then head back to Trim who will ask you to complete another quest called The Sputdye Can. For this part, you will need to head underground, into a nearby bunker. Follow the waypoint to find the Sputdye can, then bring that back to Trim also.
From that point on, Trim will be able to change your appearance in the game if you go and visit him at his shop. You will be able to change your fur coloring and fur pattern.
You will not be able to change the build, structure, or shape of your character that was established in the character creation, so you may want to keep that in mind during the creation process.