How to change the instance name of SQL Server Express 2008 R2 edition.

Make sure you have backup of all the database if you are changing the production server instance name.

1 sp_helpserver 

2 select @@servername

You can change the instance name using below query.
Default Instance

1 sp_dropserver 'old_name'

2     go 

3     sp_addserver 'new_name','local'

4 go

Named Instance

1 sp_dropserver 'Server Name\old_Instance_name'

2     go 

3     sp_addserver 'ServerName\New Instance Name','local'

4 go

Verify sql server instance configuration by running below queries

1 sp_helpserver 

2 select @@servername

Restart the SQL Server Services.

1 net stop MSSQLServer 

2 net start MSSQLServer

http://sqldbpool.com/2008/09/03/how-to-change-sql-server-instance-name/