In your child theme, open adminbar.css and add #admin-bar-logo{display:none}
that it.
Easiest way to research how is to examine the two core files responsible for the adminbar/buddybar:
buddtpressbp-corebp-core-buddybar.php & bp-core-adminbar.php
CSS is only a presentational language, display:none not the best way of hiding/removing something
to remove the site name completely add to your functions.php file in a child theme or in bp-custom.php in plugins folder this line:
`remove_action( ‘bp_adminbar_logo’, ‘bp_adminbar_logo’ );`
If you are doing a research about (display:none), no one said it’s not the best way to use it. There is a purpose for using (display:none) to hide and it does not remove it.