Set styles himself as leader of Necropolis, but in fact he's a figurehead put in place by the Master to keep the ghouls in line. Set hates the Master, but fears him more. As a result, he is frustrated and short-tempered, with a nasty tendency to lash out suddenly against any who cross him. His speech is abrupt, harsh, and so jargon-laden he is, at times, a bit difficult to understand.
Set is a rude ghoul, with one hell of a mean streak, whose colorful vocabulary consists of the extensive use of the word "dirtnap" and the phrase "standing in my shadow". According to his son, he had a bad temper before the war and ghoulification has done nothing but worsen his attitude.
In spite of Set's hostile attitude, his approach to running Necropolis appears to be one of relative non-violence, commanding his ghouls to attack only those who approach the city at night or who pose a significant threat, even allowing the underground ghouls to live peacefully in spite of being aware of their hidden location. Outsiders are permitted into Necropolis during the day, and Set himself, while volatile, aggressive, and not against harming those who anger him, tends toward honesty and favors those who express a desire to aid him and his ghoul brethren. He is quite annoyed by the super mutants. It is possible to find a note from the Lieutenant to Set, ordering him "to watch for pure-strain humans": this shows how much he disliked them by not capturing the Vault Dweller.
He is not mentioned in the Vault Dweller's memoirs, but the Vault Dweller did kill the super mutants, which led to the slaughter of almost everyone in Necropolis, including Set himself. The Café of Broken Dreams features Set among other Fallout characters: Set's dialog there suggests that his verbal repertoire may be the result of insanity such as him discussing his phrase 'dirtnap' and how he likes to say it.
Set is accompanied by a stalwart bodyguard at all times.
If the Vault Dweller completes Destroy the Super Mutants at the Watershed and then enters the vault to take the water chip, returning to Set to complete the unmarked quest will automatically make him hostile saying that the Vault Dweller "vanished the water chip".
In Ancient Egyptian mythology, Set (also spelled Seth, Sutekh or Seteh) was originally the god of the desert, storms, darkness, evil and chaos. As such, Set, leading the shady town of Necropolis, fits the reference well.
His reference to the god "Set" is also reflected in his personality; although not necessarily evil, he tends to be very aggressive.
In Fallout concept art, a person named Rake was supposed to be the Necropolis's leader.