The 'Publisher Name' field in the KDP Wizard Setting page under the expanded Barnes & Noble Options is used when asked for it on the 'Book Details > About' page when creating your book on Barnes & Noble. 

Near the end of the book listing on the 'Book Details > ISBN' page of Barnes & Noble you are asked if you have a Print ISBN for the book. If you answer 'Yes' then you'll need to provide one but if you answer 'No', then one will be created for your automatically and if you provided a 'Publisher Name' in the KDP Wizard settings page (above), this will be replaced with 'Barnes & Noble Press' instead of your own.