Sellers can't have private feedback in any case.
And only the buyer and the seller can see who bought a particular item. For all others the identities are masked.
If you want only your buyer to bid, use his ID as the title. No one else is likely to find it.
If your buyer doesn't want anyone to see what he is buying he should open a new account for his private purchases and not tell anyone the name or the password.
No one outside his friends and family cares what he is buying.