Here's an excerpt from VISA's [Card Acceptance Guidelines for Visa Merchants (PDF)](http://usa.visa.com/download/merchants/card-acceptance-guidelines-for-visa-merchants.pdf) 

> Merchant Name
> -
> 
> The merchant name is the single most important factor in cardholder
> recognition of transactions. Therefore, it is critical that the
> merchant name, while reflecting the merchant’s “Doing Business As”
> (DBA) name, also be clearly identifiable to the cardholder. This can
> minimize copy requests resulting from unrecognizable merchant
> descriptors.
> 
> Merchant applications typically list the merchant name as the merchant
> DBA. This may differ from the legal name (which can represent the
> corporate owner or parent company), and may differ from the owner’s
> name which, for sole proprietorships, may reflect the business owner.
> 
> * Keep in mind that the purpose of the merchant name is to identify the merchant to the cardholder.
> * Work with your acquirer to ensure your name is clear and discernible to cardholders when they read their statement.
> * To verify that you are using the merchant name that is most recognizable to the cardholder, compare the merchant name that you
> want to use to:  * Signage in the site photo  * Advertisements or
> brochures, and/or  * A telephone directory listing

I think that the key statement above is "*Therefore, it **is critical** that the
merchant name [...] be clearly identifiable to the cardholder.*" Since this merchant was not clearly identifiable to the cardholder, they are in breach of a critical point in these guidelines.

This is from VISA, but I would assume that all other major credit cards would have similar guidelines for their merchants. However keep in mind that these are "guidelines", and not (necessarily) rules.