Connection name: --I assume this can be anything I want?? 
Yes, the connection name can be whatever you want.
in your sites control panel, you should be able to access the database you created using PHPMyAdmin, in PHP MyAdmin, the MySQL Server address will show in the top left corner
Username: -- I assume this is the username I created when I created my database -- sitename_username??
When you create the database, you would have set a username, use that username
Password: -- I assume this is the password I created when I created the database??
when you create the database, you would have set a password to connect to the database, that is the password to enter
Database: -- When I click on select I get:
This indicates a problem in the site settings, specifically the URL Prefix in the Testing server connection settings.
make sure the URL Prefix for the testing server is correct.
