Certainly many, many kings tried to identify with Set/Seth over the course of dynastic history, so I don't know exactly how much to read into Peribsen's. Horus the Younger also claimed inheritance from Seth. I think the goal was to be considered heir of all the gods and also their collective incarnation. Typically a prince had to be content with a single role or some subset of the "divine package".
Omri, "grain gatherer", is a Joseph figure of the Kings/Chronicles narrative. He founds the pagan city of Samaria and is accused of outdoing Jeroboam son of Nebat in idolatry. The worship of Set/Baal is more explicitly associated with his successor Ahab and his Phoenician wife Jezebel. However, Omri was possibly also known as Ethbaal in Phoenicia. In my model Athaliah daughter of Omri and Jezebel daughter of Ethbaal are one and the same. The championing of Baal/Set in Israel was somewhat traditional (as it was in Upper Egypt) and may not have had much if anything to do with his Joseph typecasting.
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