This functionality occurs in Query because the Editable flag of the Name On Card field is set to 'No' in the database so the Query results will display the linked salutation in place of Name On Card. If the Editable field is set to True for the Name On Card field the results will display the same name which is displayed in Name On Card field of the membership Card. Query functionality is designed to be a grouping tool in Raiser's Edge. To report on this field users should attempt the following alternate options.
Use a Constituent Query with the same filters
Include your existing query of members in a Constituent Export. Select the desired fields in Output, including Membership > Cards > Name on Card. Be sure to enter an appropriate value (more than 3) in the field "For each Membership, enter the number of Cards to export.
As long as a large enough number is selected, all of the "Name on Card" information will be listed in the export spreadsheet correctly.