You can't make custom stats for them, but you can make portrait + name.
To make a static portrait, you can have the entire portrait in body.png
You still need to have at least one hair file and one face file, so you can just make them transparent: hair/0.png and face/0.png
You can set the name that will always be used with this portrait in params.json, it would look something like this:
{
"left": 264,
"top": 176,
"first_name": "First name here",
"last_name": "Last name"
}