How to solve the name + admin search failed?

Hello community!

I observed that a lot of businesses don’t have a dedicated branch name on their website. For example, we have the shopping center “x”. On the website are listed a lot of them across the city, and each of them has the correct address, but no mention regarding a dedicated branch name for each… people when searching for it use the name + neighborhood or name + street name, but when doing so the POI is not retrieved…
It’s there that can be done in OSM (adding alt_name with the full string name + neighborhood, etc. ) or the solution is not in OSM…

Thank you!