Displayed in the Joomla! Plugin Manager as Smart Search - Akeeba Ticket System.
This plugin integrates Akeeba Ticket System with Joomla!'s Smart Search feature (a.k.a. "Finder"). In short, it allows Smart Search to index and search public tickets. Please note that private tickets are never indexed. If you make a public ticket private it will be immediately removed from Smart Search's index.
No, we cannot have private tickets indexed and their results shown only to the ticket owner. This is a limitation of Smart Search, not Akeeba Ticket System. In order to do that we would have to create a separate Joomla! user group and a viewing access level for each and every Joomla! user. That would render your site completely unusable.