House Baratheon
Lords of Storm's End since Orys Baratheon took the castle, the girl, and the words. The house's great man of the age is Ser Lyonel, the Laughing Storm, who bellows with mirth as he fights — and fights better than nearly anyone alive.
The fuller tale
The stag is the newest sigil among the great houses and knows it — Orys Baratheon won Storm's End by killing the last Storm King in single combat during Aegon's conquest, then married the dead man's daughter and kept the old house's words for his own, a settlement that reads less like diplomacy than like a man deciding to inherit the argument along with the castle. Ours Is the Fury has stood on gold and black ever since, a motto with no patience for subtlety in a family that has generally had none to spare.
Storm's End itself supplies most of the character reference anyone needs — walls a hundred feet thick that have never once come down to siege or to the sea they face, built by men who apparently decided stubbornness was a load-bearing material. A Baratheon lord tends to govern the way that castle stands: immovable first, clever about it only when immovability alone will not answer.
The generation Dunk and Egg would have known it in belongs to Ser Lyonel Baratheon, called the Laughing Storm for a habit that unsettles most men who face him across a tourney list — he goes into a fight grinning, and comes out of it having beaten nearly everyone the Stormlands can put in front of him. It is a temperament the songs like better than the sober seriousness other great houses cultivate, and Lyonel's reputation as one of the finest lances living is exactly the kind of glory the family has always preferred to earn loudly.
Set against the black dragon's unrest elsewhere in the realm, the Stormlands in this age sit almost conspicuously settled — a great house with no attainted cousins nursing Redgrass Field grudges, no lakeside conspiracies brewing under its banners, content to let its reputation for hard fighting stay a matter of tourneys rather than treason. History would eventually ask a very different Baratheon question of a very different generation; in Dunk and Egg's day the house is simply, uncomplicatedly good at winning.
The page and the screen
Ser Lyonel Baratheon has not yet appeared as a screen character in any confirmed casting, and the Stormlands play no real part in The Hedge Knight's plot beyond geography — the house exists in this era chiefly through the novellas' passing references and the broader Targaryen-era history Martin has published separately, material the show has not needed to dramatize yet.