You can say anything. I don’t know what the name of your shop is, or whether you prefer to use brands or names to refer to shops.
However I know the names of McDs around me, even if I say that I go to “McDo” for convenience.
I know the names of multiple cinemas, even if I only usually say that I’m going to “Pathé”/“CGR”.
I say that I go to “Auchan”, even though if you ask me what is the name of this shop, it’s “Auchan X”.
Not sure what you are trying to say, apart that you prefer saying the brands of shops instead of their name. It’s totally fine, most do too, including me ! And you can display whatever you want on your OSM applications.
However, in the OSM database, the name of shops should be used as names, if presented to the public. And brands as a fallback if names are not shared, to help OSM usage. That’s what it always has been, in OSM, most of the web and world.
Edit : Tagging both the name and brand allows to best reflect what’s on the ground and digital, while still allowing each OSM user/consumer to make its own choice. Instead of forcing this choice and removing real-world data from OSM.