When you first start a new game in Kenshi you will make your first character.
Currently the only customisations available are: being male or female, being Human, two Face types and two Hair types. Skin tones range from very dark to very light.
The character editing is fairly in-depth, allowing you to manage chest broadness, shoulder width, arm bulk, hand size, neck length and width, head size, and shape independently. And for female characters you can also adjust breast size, perkiness, and shape. As for lower body modifications you can adjust overall height, posture which ranges from hunchback to English gentleman, frame bulk (Fat/Musculature), leg length and shape, hip size, feet size, waist size, stomach bulk, and mid section girth.
Keep in mind that this is very early in the development of the game and that there will likely be more races and other customization options in the future.
A hired sword for hire can be customized in the same way as your character, including their name. The same customisation screen as for the beginning character appears after hiring them. Though, players cannot change sword for hire's genders or races.