Two things:
- have you set up the SQL Alias and used that to connect SQL
- or use the DNS alias or simply server name
If you use alias then its very simple to rename.I would shut down the sharepoint, rename the server and update the SQL alias on the servers and start the SharePoint, everything will be work.
If no Alias then you have to rebuild the farm because their is no supported way to update the config db connection string.
But still you have your Content DB and Serivces db their so once you rebuild the farm then you can attach old DBs to new farm.
http://technet.microsoft.com/en-us/library/cc512725(v=office.15).aspx