I wrote:
"It's not the same king! Aren't you talking about "Pemphos" [more correctly Semempses] the "5th king of Thebes" in the list of Eratosthenes? His name is described as meaning "descendant of Herakles--whom the Greeks associated with Horus for unclear reasons."
Look at this good site and you can see where this list of Eratosthenes got "Smsw" or "smsm". It is king Smerkhet of Dynasty One. As Horus is on his standard after the cartouche, he became involved.
https://pharaoh.se/turin-papyrus-king-list