add_filter( 'woocommerce_checkout_fields' , array($this,'checkout_extra_fields'));
public function checkout_extra_fields($fields){
    $fields['billing']['vat_number'] = array(
        'label'       => __('VAT number', 'my-slug'),
        'placeholder' => __('VAT number', 'my-slug'),
        'required'    => false,
        'clear'       => false,
        'type'        => 'text',
    );

    $fields['billing']['commerce_number'] = array(
        'label'       => __('Commerce number', 'my-slug'),
        'placeholder' => __('Commerce number', 'my-slug'),
        'required'    => false,
        'clear'       => false,
        'type'        => 'text'
    );

    return $fields;
}