1. Login on to the server you want to change the name of 

2. Run this in Microsoft SQL Server Management Studio
3. Click on Create New Query
4. Enter this code to get the existing name.
select @@servername
5. After code is entered click the red exclamation point to execute
6. The current name will be returned. 
7. Next enter the following text filling in the appropriate information for you environment.
sp_dropserver 'old_name'
go
sp_addserver 'new_name','local'
go
8. After code is entered click the red exclamation point to execute
9. Now close Microsoft SQL Server Management Studio
10. Run the command prompt Administrator and run the following two commands
net stop mssqlserver
net start mssqlserver
11. Now reopen Microsoft SQL Server Management Studio and rerun
select @@servername
 
12. Make sure the name matches the ‘new_name’