Hiding the name of the user who is currently editing

The avatar and text is set in wp-admin/includes/class-wp-posts-list-table.php. It’s not directly filterable, but it’s possible to use JavaScript to target them and change since they each have their own class names.

For avatars, target .locked-avatar, the text is inside .locked-text.

The text itself is translatable on the PHP side, so it’s possible to filter gettext calls to change the string before it’s displayed, but that will only get the text, not the user’s name or avatar, so I suggest going with CSS/JS on the front end first.