Is a merchant required to display the Visa logo? Yes. This is clearly outlined in the Visa Card Acceptance Guide. Merchants must display the Visa logo at the merchant location or on catalog, sale materials, or websites.
So, if you do not have the logo on your catalog order form, or your web site, you are not in compliance with card association rules. Refer to page 9 of the Card Acceptance Guide aka Card Acceptance and Chargeback Management Guidelines for Visa Merchants.