Problem

I could not update the billing address on an invoice as described above.  In my case, the customer was a sub-customer of a parent company.  The contact name for my sub-customer kept appearing in the billing address.  I could edit the address and delete the name, but when I clicked Save, the contact name reappeared.

Support
I chatted with support about this.  They were slow, didn't fully understand the problem, were not fluent in English, and could not provide any help.  I provided screen shots, tried multiple browsers, and cleared cookies at their prompting, but none of these convinced them that the software was doing something unhelpful.

Solution

I was able to get around the software's behavior.

• Edit the Customer
• Enter the Name of the parent company in the Company field
  (this is the name that will appear on the invoice)

You can keep the sub-customer's contact name in the [Display name as] field if you'd like to.

Now, the invoice will accept having just the company name, without the sub-customer contact name visible, and I can edit the billing address as needed, per invoice, without editing the customer record.

I hope that helps with your scenario.

Cheers