Pimcore\Model\Element\Tag::getNamePath PHP Method

    public function getNamePath($includeOwnName = true)
    {
        //set id path to correct value
        $parentNames = [];
        if ($includeOwnName) {
            $parentNames[] = $this->getName();
        }
        $parent = $this->getParent();
        while ($parent) {
            $parentNames[] = $parent->getName();
            $parent = $parent->getParent();
        }
        $parentNames = array_reverse($parentNames);
        return "/" . implode("/", $parentNames) . "/";
    }

 protected function convertTagToArray(Tag $tag, $showSelection, $assignedTagIds, $loadChildren = false)
 {
     $tagArray = ["id" => $tag->getId(), "text" => $tag->getName(), "path" => $tag->getNamePath(), "expandable" => $tag->hasChildren(), "iconCls" => "pimcore_icon_element_tags", "qtipCfg" => ["title" => "ID: " . $tag->getId()]];
     if ($showSelection) {
         $tagArray["checked"] = isset($assignedTagIds[$tag->getId()]);
     }
     if ($loadChildren) {
         $children = $tag->getChildren();
         foreach ($children as $child) {
             $tagArray['children'][] = $this->convertTagToArray($child, $showSelection, $assignedTagIds);
         }
     }
     return $tagArray;
 }