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. 

All Customer facing documents will only show the CUSTOMER version of the product. This includes the Customer Invoice.