WordPress needs a database to work, so if you have a WordPress site, you must have a database as well.
However, there is currently a bug in the system. If you install a script with Softaculous, a database is created, but this database doesn’t show up in the MySQL Databases and phpMyAdmin sections in the control panel. To make the database appear, you can find the database name in the installation details in Softaculous, and then use the MySQL Databases section in the control panel to “create” a database with the same name.
I just did that, and you can now see a database with the suffix _w120 in the control panel.