If I understand correctly, you want to accept PayPal payment on your site, but use the PayPal email address of the company whom you're an affiliate of to receive the actual payment.
If that's the case, you would need the cooperation of that company to review the "Details" for their sales, in which you can specify your affiliate ID in the item's "Description" or elsewhere. I doubt however that a site with significant sales would want to do that however as it would require manual review, or some programming to track the ID in an exported sales CSV.
Affiliates usually do not accept payment directly on their sites. Instead they link or redirect customers to the company's site you're an affiliate of, who tracks the sale by affiliate ID, or employs a third-party site to do this for them (e.g.,
So in short, I do not think you can expect the company to be able to track purchases made on your site as you indicated.