Who is the king of Surat Al-Kahf?

It is not clear what is meant by the question about the king. Is it the king during whose time the People of the Cave went out, or the one during whose time they emerged, or Dhu al-Qarnayn? Historians mentioned that the People of the Cave went out during the time of King Barbarus and emerged during the time of King Decius. As for Dhu al-Qarnayn, there is disagreement about his name, and a hadith states that he was from Himyar and his mother was Roman. We should note that if there were any benefit in mentioning their names, the Quran would have mentioned them. The lesson and benefits lie in their stories.