>When I installed SQL Server, I selected the default name of the server and instance. Is it possible to change that after?
My personal opinion would be to uninstall the instance and reinstall. I've done that a few times (where I didn't specify the instance name the way I wanted it...usually when I was creating a VM).
Now, there are system stored procs sp_dropserver and sp_addserver. They are discussed in these two links: