In standard Odoo, the functionality you’re looking for is already available. If you have defined the vendor's product name and code under the Purchase tab of the product, this information will automatically populate in the Description field of the Purchase Order line whenever the product is selected. This description is then fetched and displayed in the Purchase Order printout.

If no vendor product name or code is defined, Odoo will default to using the product's name and internal reference in the description field, which will consider for printout.

Please check the following:

1. Verify if you’ve defined the Vendor Product Name and Vendor Product Code for the product.
2. Ensure that the Purchase Order report has not been customized, as customizations might override the default behavior.