Here is a sample command for renaming a domain-joined computer. Note that to run this command you will need a user account that is a local admin on the remote machine and that has sufficient permissions in active directory to change the computer name:
netdom renamecomputer <computer_name> /newname:<new_name> /userd:<domain>\<username with privilige to do the rename> /passwordd:<password of account> /force /reboot:120
Note that the above command will perform a reboot after 2 minutes, which may not be what you want.
Watch out for things like the password - note the switch is /passwordd, not /password.
Edit - I initially wrote that netdom was a Sysinternals utility, but it is part of the Windows 7 RSAT.
The Fixed Machine Name is the current name of the computer. Some services use the machine name to reference resources running locally instead of using an IP address or localhost.
For example some SQL services use the machine name for accessing their databases, so if you were to change the machine name the SQL service wouldn't know how or where the database would be any more and anything relying on the SQL service would not run correctly.
If you do not have any services or resources that use the current machine name for referencing data locally then there should be no problem with changing the computer name.