I have installed SQL Server 2008 R2 Developer edition successfully. I have 2 problems
Its showing 2 (local) servers in server nameA network-related or instance-specific error occured while establishing a connection to SQL Server. The server was not found or was not accessible. Verify that the instance name is correct and that SQL Server is configured to allow remote connections. (provider: Name Pipes Provider, error: 40 - Could not open a connection to SQL Server) (Microsoft SQL Server, Error: 2)

If you installed as a default instance then local will work else named instance you have to connect by servername and instance name . you can browse for instance name in connect to window pop up too.
Check your sql configuration wizard weather sql service is running.