You have 40 chars available for in the name field for USPS (35 for FedEx and UPS) - fit it there if possible (with abbreviating too as needed)
Otherwise, put it on the second address line.
USPS doesn't care, and this is such an edge case need (1 in thousands) that there is realistically no chance eBay is going to change it.
PayPal labels doesn't have a provision for it either. Nor Amazon or UPS.com USPS.com and FedEx.com do have a "Company" field that can be used for that purpose.
Maybe in some iteration of the label flow some day someone will say "hey that would be a good idea", but that might also be contingent on the Pitney Bowes APIS. USPS APIs most certainly support a second name field (Company), but it's possible that the Pitney Bowes
(eBay's and PayPal's label provider) APIs do not. If so, eBay can't add a new data field. (ebay Label Flow → Pitney Bowes API → USPS API)
In any case, I can pretty confidently say that it isn't going to be changed because you asked 
[Addendum]
The new eBay label flow does have a "Company" field that you could use for that if you edit the buyer's address.
So I guess a non-issue then.
