Unlike your farm name that you can change in your game’s settings, the roadside shop name comes from your Facebook name, your Gamer ID or your Game Center nickname, depending on which account your farm is attached to.
With Facebook it is not possible to change your roadside shop name unless you change your name in your Facebook app.
With Game Center, you can simply go in to your device’s settings > Game Center > Nickname.
With Google + just go to your Google play games app and change the Gamer ID.
Once you have changed and saved the new name, it will be seen as your roadside shop name.