That does not seem to be the case in France, or in the UK, or the USA, or Italy. You get the gist. I’ve yet to find a store chain that does not distinguish publicly between their store.
The Name Suggestion Index project, which helps ensure consistent brand and operator tagging, generally includes only the brand name in
name=*,
The NSI, while really useful most of the time, degrade OSM regarding the name of chain brands sadly.