I'm not sure - trademark law is tricky - "The Container Store" is trademarked (and while you might say "App Store" is too generic, but I don't recall the term existing prior to "The App Store", so this might be a "Hoover" or similar situation).
I remember McDonald's used[?] to have "All Beef" as a trademark for their burger patties (I also recall them getting in trouble in NZ as just because they're "All Beef" brand doesn't mean you can advertise them as "All Beef Patties" in a way that is clearly intended to imply they're "all beef")
App Store is not the same case as Hoover because the name is a literal description of what it is. It’s like a coffee producer trademarking the name Coffee.
I remember McDonald's used[?] to have "All Beef" as a trademark for their burger patties (I also recall them getting in trouble in NZ as just because they're "All Beef" brand doesn't mean you can advertise them as "All Beef Patties" in a way that is clearly intended to imply they're "all beef")