I think this is a bug and not intentional, but renting the shop in the screenshot gave me ownership of the shop next to it as well. Naming one shop would change the name of the other, both shop signs accessed the same shop. It did NOT dupe items from one shop to the other, each table saved items independently (Noting this so you know it's not super urgent to fix).
Another issue with some of the shops is it's hard to access their inventories. These 3 seem to be the worst:
This shop in particular could be fixed by making the shop inventory a clickable table like the other clickable tables in the area. In the screenshot you can see that it has a click point, rather than the table placeable itself being interactable.
