In A Knight of the Seven Kingdoms (the Dunk & Egg stories), the ruling king at the time of the events is King Daeron II Targaryen , known as “Daeron the Good.”

Later in the larger lore, Dunk’s young squire Egg grows up to become King Aegon V Targaryen (“Egg”), but that happens after the period covered by the early Dunk & Egg tales on which the show is based.