Apparently my registry is somewhat different than what is described by Mr. Miller and the websites suggested by Mr. Harris. I was successful using the combination of their suggestions that I have listed below
Although this technique worked for me, the bottom line is that it really shouldn't be such a pain to rename the desktop icons. You should be able to right-click, select rename and go from there. (In fact you can do that, but it reverts next time your restart the computer.
Despite my complaints, thanks for the help
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In Regedit navigate to HKEY_CLASSES_ROOT/CLSID
Then navigate to the registry branch shown below for the icon you want to rename
My Network Places {208D2C60-3AEA-1069-A2D7-08002B30309D}
My Computer {20D04FE0-3AEA-1069-A2D8-08002B30309D}
My Documents {450D8FBA-AD25-11D0-98A8-0800361B1103}
Recycle Bin {645FF040-5081-101B-9F08-00AA002F954E}
Internet Explorer {871C5380-42A0-1069-A2EA-08002B30309D
In the right panel, right-click on "LocalizedString" and rename it to "LocalizedString.old
Right-click in an empty area of the right panel, select Expandable String Value and name it "LocalizedString
Double-click on the new "LocalizedString" and in the Value data field enter whatever name you want for the icon
Click OK, then right click on your desktop, select Refresh and you should see the new name for the icon.