The layers in the controller.
It's important to note that the AnimatorControllerLayer are returned as a copy. The array should be set back into the property when changed.
class ControllerModifier
{
    UnityEditor.Animations.AnimatorController controller;
    public void ModifyLayers(int layerIndex, string newName)
    {
        UnityEditor.Animations.AnimatorControllerLayer[] layers = controller.layers;
        layers[layerIndex].name = newName;
        controller.layers = layers;
    }
}