Windows 7 puts numbers after my wireless network name

Hello. I don't know how exactly to explain my problem but I'll try:
I connect to a wireless network whose name is for example "X" and I have a network connection but I don't have internet access. I disable and enable the wireless adapter and the name of the network is now "X 1" and so on... The problem is my internet is only working on number 9 and I don't know how to delete the other available settings (I am not sure if they are settings) so I can connect only to number 9, not to all other numbers to 10 in different orders - I mean if I disable/enable once it gives me a lucky number - not one after another. I don't know if you understood what I mean but I really hope so. Thank you

No, it doesn't rename it there. I told you I can't exactly describe my problem. I'll try like this:
You know where it says under the icon of your Network adapter "Enabled/Disabled"? This is where it puts numbers. The name of the network I am connected to is displayed as it's name is when I open "Properties". This is the only place I see this 1, 2, 6, 10 thing. And of course when I connect and I point on the icon in the tray where the wireless is it says "X 9" Internet access
Hope you got my point now

Wireless network "X" is just one. There are other 2 in the list but these I use at home and university.

No. It's a local internet service provider and it's unsecured network. You sign in with a user and pass in their website to get internet access.

I think I know what the OP is trying to explain. He's talking about the name given to your Local Area Connection under Connect or Disconnect in the Network and Sharing Center. I've seen this happen it you have a USB wireless dongle and move it from one USB port to another. Windows doesn't consider it the same device, it loads the driver as if new hardware was detected and you end up with "Wireless Network Connection 2", if you move it yet again you get "Wireless Network Connection 3". If you go into device manager and "show hidden devices" you'll see them all listed under Network Adapters. I've seen it in windows XP and if you try to uninstall one of them it fails with a "this device may be needed for your PC to boot up". <Something like that anyway. After a lot of screwing around I found that if you uninstall the QOS packet scheduler you can then uninstall the extra network adapters in device manager.