It's showing you the service name, not the instance name.

>You are absolutely correct. Both (local) and using my computer name as the SQL Server name works. But what is confusing is that in the SQL Server Configuration it says that MSSQLSERVER is running. What is then the difference between the MSSQLSERVER (which I remember seeing as the name of the server during the installation) and the computer name as the SQL Server name?
>Thank you.