Change SQL Server Name

1. Open SQL Server Management Studio and click New Query.
2. Type Select @@ServerName to find out the current server name. In our example, we’ll be changing the server name from RKF to REH.
3. Next, type sp_dropserver ‘RKF’
4. You are now ready to add the correct name by typing sp_addserver ‘REH’.
5. Stop sql server and the sql server agent by opening a command prompt and typing net stop mssqlserver. 
6. Restart SQL server by typing net start msssqlserver.
7. Restart SQL server agent by typing net start sqlserveragent.
8. Click New Query in SQL Server Management Studio and type select @@servername to verify everything is correct and you have successfully changed the sql server name. 

https://community.dynamics.com/product/gp/gptechnical/b/gplesliev/archive/2012/02/02/change-the-name-of-the-sql-server.aspx