This is supported the same way you setup Vendor specific Product Codes.

First, define a custom Inherited View that uses the Context attribute to set the partner_id key:

<field name="order_line" position="attributes">
    <attribute name="context">{'partner_id': partner_id}</attribute>
</field>

Note: be sure to check that the sale.order.form View you are inheriting is the one with the External ID equal to sale.order.form

Next, setup the information in the same way. On the Purchase tab of the Product, below your Vendors if applicable, add a line for each Customer with the unique Product Code and/or Product Name. 

The Customer Preview and PDF report of the Sales Order and the Customer Preview and PDF report of the Customer Invoice will only show the CUSTOMER version of the product. 

If you also require this information on the Delivery Order, you will need another customized view that adds it there:

<span t-out="aggregated_lines[line]['name']" position="replace">
    <span t-if="aggregated_lines[line].get('product')" 
          t-esc="aggregated_lines[line]['product'].with_context(partner_id=o.partner_id.id).display_name"/>
    <span t-else="" t-esc="aggregated_lines[line]['name']"/>
</span>

If your Delivery involves packages and/or serial numbers you may need to modify the second view accordingly - your Odoo Digital Advisor or Odoo Partner can help here.