From looking at your cPanel setup, it looks like you created a MySQL database, but there are no database users assigned to it, which essentially means the database is inaccessible. Most installation software requires a database name, which you'd be able to provide since the database is already created, but when it asks for a user and pass, you don't have one yet.
Go into the MySQL databases section in cpanel, and add a new user; you'll be able to specify a password for that user, which you'll want to remember for the installation later. Once you've created the new user, go to the bottom under "Add User to Database"; select the user you just created, the database you've created, and select Add. On the next screen, mark the box for "All Privileges," then next, and the user will be added to the database. This should allow you to install the software, as you'll now have a username/pass that you can enter when asked for it, which will allow the software to connect to the database properly.