Hi,

If you have a default instance , you can rename it to whatever following the steps above. ( Default instance means the instance name = hostname of the server ).

BUT, if you have a named instance  (i.e ) while setting your server up you add a new name like say testinstance , then when SQL Server is installed  the instance name will be
hostname\testinstance. In this case you CANNOT change the instance name and would need to UNINSTALL SQL server and reinstall it.

Thanks,