Renaming the physical server hosting your SQL Instance is definitely possible, here's how MS suggests doing it since you'll need to also update the metadata in SQL after the change:

http://msdn.microsoft.com/en-us/library/ms143799.aspx

Something to note depending on what services your using is this may affect kerberos. Just test anything that does a double-hop back to the server like Reporting Services or SSIS to verify they still work after the rename. If not you'll need to modify your SPNs.