Everyone here has a write-up, drawn from the same records that explain the names while you read the text.
Saul
King of Israel, before the splitIsrael's first king, given when the people demanded one 'like the nations.' Tall and promising, Saul started well but unraveled, offering an unlawful sacrifice, sparing what God had devoted to destruction, and hunting David out of jealousy. Rejected by God through Samuel, he ended by consulting a medium and falling on his own sword at Gilboa.
1 Samuel 9-101 Samuel 151 Samuel 31Study → David
King of Israel, before the splitThe shepherd-poet who killed Goliath, outlasted Saul's jealousy, and united the tribes with Jerusalem as his capital. A man after God's own heart, yet his adultery with Bathsheba and its cover-up cost him dearly. God promised his throne would endure forever, the covenant the Messiah would fulfill.
1 Samuel 16-172 Samuel 5-72 Samuel 11-12Study → Nathan
Prophet in David's courtThe prophet who brought David both the covenant promise of an everlasting throne and, later, the parable of the poor man's lamb that trapped the king into condemning himself.
2 Samuel 72 Samuel 12:1-151 Kings 1
Phinehas
Two priests of this nameEleazar's son, who ended a plague at Peor by driving a spear through an Israelite man and a Midianite woman, and was granted a covenant of lasting priesthood. A second Phinehas, son of Eli, was a corrupt priest who died carrying the ark into battle.
Numbers 25:6-13Joshua 22:13-34Judges 20:28
Korah
The rebellionA Levite who led two hundred and fifty leaders in challenging Moses and Aaron, arguing that the whole congregation was holy and the two of them had exalted themselves. The ground opened and swallowed the ringleaders.
Numbers 16:1-35Numbers 26:11Psalm 42 heading
Zebah
The Midianite kings and princesThe four Midianite leaders Gideon's campaign brought down. Oreb and Zeeb, whose names mean raven and wolf, were killed at the rock and the winepress that afterward carried their names. Zebah and Zalmunna were pursued far east and taken.
Judges 7:25Judges 8:4-21Psalm 83:11
Abimelech
King of GerarA Philistine king of Gerar, in the Negev, who took Sarah into his household after Abraham passed her off as his sister, and was warned in a dream before he touched her. He confronted Abraham about it with a fairness that puts the patriarch in a poor light.
Genesis 20:1-18Genesis 21:22-34Genesis 26:1-33
Sihon
Kings east of the JordanTwo Amorite kings, of Heshbon and of Bashan, who refused Israel passage and were defeated. Their names become a fixed pair in Israel's memory, recited in psalms and speeches for centuries as the standard example of what God did.
Numbers 21:21-35Deuteronomy 3:1-11Psalm 136:17-22
Ahithophel
The counselor who turnedDavid's advisor, whose counsel was regarded as if a man had inquired of the word of God, and who went over to Absalom's revolt. When his advice to strike immediately was set aside for worse advice, he went home, set his house in order, and hanged himself.
2 Samuel 15:12-312 Samuel 16:20-17:23Psalm 41:9
Asaph
The temple musiciansThe men David appointed to lead music before the ark, and the guilds descended from them who ran worship in the temple for centuries. Twelve psalms carry Asaph's name, and others carry Heman's and Ethan's.
1 Chronicles 6:31-331 Chronicles 16:4-71 Chronicles 25:1-6