Wired connection takes on wireless name

I was recently doing some testing on a Vista machine, and decided to shut down the wireless adapter and use the Ethernet jack temporarily to see if it made a difference with what I was testing. It didn't, but in the process I would get somewhat confused because the wired connection would show up in the Network Center using the name of my wireless network each time I'd connect it. How do I get the machine to use a different name for each connection? Or is this not possible because both connections are (in my case) accessing the same network? And if not, how do I change the name it uses so that it doesn't seem so wireless-specific?
 

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