That was already answered in the thread in the last messages.

>you have to tag it as the majority of mappers would

Can you point me to rules that prescribe that ?

To the contrary, OSM is a healthy community of diverse mappers. Diversity, in opinion here, is paramount to the project, to allow it to adapt to local specificity and grow. And that is reflected on multiple OSM wiki pages. 

Sure, some contributions actively harm the project and usability, but you'll agree that's absolutely not the case, it's a minor disagreement.

Having the name chosen and displayed everywhere by the shop, and used by local people on the ground is the best one to use.

The "use the biggest name [not brand]" suggestion is targeted where there is "real" disagreement on the name (local vs government choices, multilingualism etc.).

There is no downside to using the name chosen by the shop. The renderer and consumers can make any choice they want.

Here the commenters prefer rendering the brand instead of the name on the map; they can do so easily. I'm available if they need help configuring their map style for that.