Change machine name of a client from DC?

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http://serverfault.com – I'm granting least privileges needed for an account, that he could rename the computer machine name for each client. (All Windows 7 PCs) These clients have already joined the domain, now what kind of privileges should I grant to that account? Not the domain admins group, of course. Also I tried to grant full control of Computers objects to that account, but when I navigated to the Computer Properties tab, on Advanced System Settings tab, I clicked the button and it still asks for password of a Domain Admin account. What's the right way to do so? (HowTos)