Once you have installed your ConfigMgr Primary Site it is not possible to change the name of your Primary Site. At least not through the console… But what if you made a mistake or your company changes it’s naming conventions?? Well there is one way to change it. First off all stop the SMS_EXECUTIVE Service. After that open the site control file (<Installation directory>\Microsoft Configuration Manager\inboxes\sitectrl.box\Sitectrl.ct0) and search for BEGIN_SITE_DEFINITION. Close to that you will find your Primary Site name and you can change it (do not change anything else!!). After this save the file and start the SMS_EXECUTIVE Service again. Then after a few site refreshes your Primary Site name wil be changed.
In some cases it could be possible that you also have to change the value of the regkey: HKLM\Software\Microsoft\SMS\Identification.
Update: Keep in mind that editing the sitectrl.ct0 is not supported by Microsoft!