You’ll have to hook into the event from your website and send it as an additional field. It’ll be difficult to give specific help as it may also be theme and plugin dependent. 

Basically, before the event is sent to Klaviyo, you need to interrupt it and pull that field into the ‘extra → billing address’ array.

Hi David, thanks for your message! I appreciate your reply and your willingness to help.

I don't see a way to adjust this in WordPress. Or is there an option?

There’s no easy way to do this. It has to be handled directly in your PHP code so you’ll need a developer to do it.

We have made custom code for this. And i see the Company value in the array in Klaviyo. But it doesnt get aded to the profile so maybe the array is wrong or Klaviyo wants the company on a different location? 

See code below:

add_filter('kl_started_checkout','kl_modify_started_checkout', 1, 2);

function kl_modify_started_checkout($checkout_data, $cart){
    $company = WC()->checkout()->get_value('billing_company');

    $checkout_data_'$extra']t'BillingAddress']e'Company'] = $company;
    return $checkout_data;
}