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Some Internet service providers (ISPs) require you to use a specific computer name so they can identify your computer and validate your account. If your ISP requires a specific computer name, don't change the name they give you ..
When you type the new name and push OK on the Computer name/domain dialog, does the "computer name" back in System Properties Computer Name change at that time, or not?
I know it should then say that you must reboot for the changes to be applied, but even before reboot the System Properties Computer Name dialog should reflect the name change you just made in the Computer name/domain dialog.
So then, after you reboot, are you saying the old name has returned, and the supposed name change which appeared to work before the reboot has now just vaporized, and that the original name is still there?