This remote return only the trait names from the current class.

If your class extends another class using your trait, you can't get the names. However, you can do something like :

<?php
$traitsNames = [];
$recursiveClasses = function ($class) use(&$recursiveClasses, &$traitsNames) {
    if ($class->getParentClass() != false) {
        $recursiveClasses($class->getParentClass());
    }
    else {
        $traitsNames = array_merge($traitsNames, $class->getTraitNames());
    }
};
$recursiveClasses($controllerClass);