Hello, again. The reason why "My Auchan" is considered a different chain, is certainly because "Auchan" (at least, here in Portugal) is usually a chain of so-called hypermarkets (like the one that exists at the local mall: https://www.openstreetmap.org/node/485243343). And, these "My Auchan" stores are (much) smaller than Auchan's hypermarkets. So, the slightly different name is certainly a way to indirectly tell people not to expect these "My Auchan" stores to be regular Auchan stores (i.e. hypermarkets). But still, at least when it comes to the two stores I've visited again, I definitely wouldn't call them convenience stores, but supermarkets instead. (And, from my experience, I think that a good classification for these store's sizes would be something like: small = convenience store; medium, even if lower type of medium = supermarket; big, and very big = hypermarket. But, I see that the last term doesn't exist in OSM's tags.)