The following steps are necessary for renaming the computer or changing the domain:

Step 1: Update Alternative Access Mappings
a. Open Central Administration -> Operations -> Alternate access mappings
b. Modify each mapping item to reflect your newly chosen server name (<newname>)

Step 2: Use stsadm to migrate ConfigDatabase
a. Open a command prompt window
b. Go to the 14-Folder/BIN: C:\Program Files\Common Files\Microsoft Shared\web server extensions\14\BIN
c. Execute: stsadm.exe –o renameserver –newservername <newname> -oldservername <oldname>

Step 3: Rename your Server
a. Open System, “Computer Name” tab, Change button
b. Input your new server name <newname> / domain name
c. Reboot the server NOW

Step 4: Update Central Administration Webapp-pool
a. Open a command prompt window
b. Go to the 14-Folder/BIN: C:\Program Files\Common Files\Microsoft Shared\web server extensions\14\BIN
c. Execute: stsadm.exe –o updatefarmcredentials –userlogin <FARMADMINUSERNAME> -password <FARMADMINPASSWORD>
This is necassary if the account has changed (lokal computer account is used or domain has changed)

Step 5: Update IIS Apppool Accounts
a. Open Internet Information Services and check if all AppPools run with the user in the new Domain or new local computer name

Step 6: Update Central Administration Service accounts
a. Open Central Administration
b. Go to Operations\Service accounts
c. Modify all WebApplication users to run within the new user name

Step 7: iisreset

Now the SharePoint server is renamed and the SharePoint 2010 should work again.