You mean the AirPort Menu Bar icon. Right? Since I think this is the case I'll give you information on why that is showing up.
The AirPort menu displays all wireless networks that it detects if they have a Secure Set Identification (SSID) that is enabled to be visible. (An SSID is basically the wireless network name that a wireless network has.) The reason why you are seeing your SSID and anther SSID is because you are in a region where you can pick up another wireless network. There is no way to get rid of it unless you move away from your neighbor's wireless network.
But the AirPort menu is only designed for people who move from place to place often. Is there any reason why you wanted to get rid of your neighbors SSID on your AirPort menu? There is no reason why you need to use the AirPort menu again if you already connected to your home network once.
If you want to automatically connect to a wireless networks of your choice in various locations I can take you through the steps to make it possible.