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This person receives your product but they MAY or MAY NOT be your customer (maybe someone who can deliver it to your customer like their relative or friends but not some delivery company). Also, their details are added to under 'Shipping Details' by the customer maybe because your customer doesn't have a permanent address yet.
What do you call this person? Some names I thought of were 'receiver' or 'referee' or 'trustee' but I don't think they're accurate enough in business terms.
If this person actually has their name and address as the "Ship To" address then they may be referred to as the addressee (the one to whom it is addressed).
Alternatively, the package may be addressed to your customer in the care of some intermediary.
From Wiktionary:
Care of, usually abbreviated as c/o on envelopes, signifies an intermediary* who is responsible for transferring a piece of mail between the postal system and the final addressee. For example, when the addressee has no standard address, is under a corporate mail system, or is being manually forwarded mail sent to a more accessible location.
* emphasis mine
A recipient (as defined by say Lexico) is what you call someone who receives something. It would fit the context.
Since you are specifically talking about shipping a product sold, another often-used term is consignee, an -ee derivation to the verb consign (same link, def. 1.1):
Send (goods) by a public carrier.
The consignee of a package is the person to whom it is addressed. Unlike recipient and addressee (which are both perfectly valid words for this, but also have broader meanings in other contexts), consignee is very rarely, if ever, used to refer to anything but specifically the recipient of a (commercial) shipment or package.
Recipient
Dictionary.com:
a person or thing that receives; receive
Cambridge dictionary:
a person who receives something
Merriem-Webster:
one that receives : RECEIVER
Vocabulary.com:
the person on the receiving end of something.
Macmillan:
someone who receives something
