The fact that another application is working does not mean much beyond confirming that you have SQL Server installed. The problem seems to be that SQL Server is installed in a way that the BV Site Manager does not recognize.
re named versus unnamed instances: you can install multiple instances of SQL Server. One can be unnamed. In that case the server name is "." or "localhost" or "COMPUTER-NAME" (where COMPUTER-NAME is the name of your computer). You can install as many named instances as you want. The server name for a named instance is ".\INSTANCE-NAME", or "localhost\INSTANCE-NAME", or "COMPUTER-NAME\INSTANCE-NAME".
If you don't recall naming the instance, then you probably have one unnamed instance installed. In that case, you would use ".", or "localhost", or "COMPUTER-NAME" as the SQL Server name in the BV Site Manager.
That instance must be configured to accept TCP/IP connections. To check, launch the SQL Server Configuration Manager, expand SQL Server 2005 Network Configuration, then click on the instance you are targeting. If TCP/IP is not enabled, then enable it.
I'm not sure, but I think the target instance must also be configured to allow remote connections. To to this, launch the SQL Server Surface Area Configuration tool, make sure your target instance is selected, then select Surface Area Configuration for Services and Connections, expand Database Engine, select Remote Connections, then select Local and remote connections using TCP/IP only or using both TCP/IP and named pipes.
You also need the SQL Server Management Objects installed. You can find links to those here,
http://www.bvsoftware.com/downloads/SQLXMO/Finally, the username and password that you use must have permission in the target instance to create a database, tables, etc.