The instance name is needed only if you want to connect to a named instance.
If your install of Sql Server hasn't created a named instance then the default for the instance is MSSQLSERVER
and you DON'T need to specify that part on the connection string.
However, the computer name part is required but it could be expressed in various form
- a point to mean the local computer
- an IP address (local or not)
- a server name recognized by the DNS system of your lan
- the special string (LOCAL)
More info on the Data Source key could be found on MSDN docs for ConnectionString