I think it's "Abandoned Shed", but I don't know if buying it changes the name to something like "Shed", or "%PLAYER_NAME%'s Shed" since it's no longer abandoned once bought.
I think you can build a new floor, unconnected to the shed, on your land, and you should get a system pop up to name the new building, and it should have the name of the area/shed as default. Otherwise, I don't know.