Among the kings of the Northern Kingdom of Israel, started by the supporters of king Saul, 4 of them ruled from a town named Tirzah (Baasha, Elah, Zimri and Omni).
Numerous towns were named after people. In this case, only one person named Tirzah was found in the Bible. She was one of 5 daughters of Zelophehad (a descendant of Jacob's son, Joseph).
Post-Flood lineage: Jacob (Israel) > Joseph > Manasseh > Makir > Gilead > Hepher > Zelophehad
The daughters of Zelophehad mainly appeared during the conquest of Canaan. The book of Numbers had 3 passages about them where they secured land for themselves since their father had no male heirs.
Numbers 26:33:
28. The descendants of Joseph by their clans through Manasseh and Ephraim were:
29. The descendants of Manasseh: through Makir, the Makirite clan (Makir was the father of Gilead); through Gilead, the Gileadite clan.
30. These were the descendants of Gilead: through Iezer, the Iezerite clan; through Helek, the Helekite clan;
31. through Asriel, the Asrielite clan; through Shechem, the Shechemite clan;
32. through Shemida, the Shemidaite clan; through Hepher, the Hepherite clan.
33. (Zelophehad son of Hepher had no sons; he had only daughters, whose names were Mahlah, Noah, Hoglah, Milcah and Tirzah.)
Numbers 27:1-3:
1. The daughters of Zelophehad son of Hepher, the son of Gilead, the son of Makir, the son of Manasseh, belonged to the clans of Manasseh son of Joseph. The names of the daughters were Mahlah, Noah, Hoglah, Milcah and Tirzah. They approached
2. the entrance to the Tent of Meeting and stood before Moses, Eleazar the priest, the leaders and the whole assembly, and said,
3. "Our father died in the desert. He was not among Korah's followers, who banded together against the LORD, but he died for his own sin and left no sons.
Numbers 36:11-12:
11. Zelophehad's daughters--Mahlah, Tirzah, Hoglah, Milcah and Noah--married their cousins on their father's side.
12. They married within the clans of the descendants of Manasseh son of Joseph, and their inheritance remained in their father's clan and tribe.
After Moses had died and Joshua had led a successful campaign against several tribes of Canaanites, a town named Tirzah was stated in Joshua 12:24 among the defeated kings.
Joshua 17:1-6 told of the territory of Manasseh within the conquered lands:
1. This was the allotment for the tribe of Manasseh as Joseph's firstborn, that is, for Makir, Manasseh's firstborn. Makir was the ancestor of the Gileadites, who had received Gilead and Bashan because the Makirites were great soldiers.
2. So this allotment was for the rest of the people of Manasseh--the clans of Abiezer, Helek, Asriel, Shechem, Hepher and Shemida. These are the other male descendants of Manasseh son of Joseph by their clans.
3. Now Zelophehad son of Hepher, the son of Gilead, the son of Makir, the son of Manasseh, had no sons but only daughters, whose names were Mahlah, Noah, Hoglah, Milcah and Tirzah.
4. They went to Eleazar the priest, Joshua son of Nun, and the leaders and said, "The LORD commanded Moses to give us an inheritance among our brothers." So Joshua gave them an inheritance along with the brothers of their father, according to the LORD's command.
5. Manasseh's share consisted of ten tracts of land besides Gilead and Bashan east of the Jordan,
6. because the daughters of the tribe of Manasseh received an inheritance among the sons. The land of Gilead belonged to the rest of the descendants of Manasseh.
Several instances of the town Tirzah showed in the book of 1 Kings. 1 Kings 14:17 spoke of the death of Jeroboam's son in that town. It was also mentioned twice in 1 Kings 15 in verse 21 when the Aramean king, Ben-Hadad, and the Southern Kingdom of Judah's king, Asa, allied against Baasha, the king of the Northern Kingdom at the time, then again when Baasha's rule ended in verse 33.
1 Kings 16:8-17,23:
8. In the twenty-sixth year of Asa king of Judah, Elah son of Baasha became king of Israel, and he reigned in Tirzah two years.
9. Zimri, one of his officials, who had command of half his chariots, plotted against him. Elah was in Tirzah at the time, getting drunk in the home of Arza, the man in charge of the palace at Tirzah.
10. Zimri came in, struck him down and killed him in the twenty-seventh year of Asa king of Judah. Then he succeeded him as king.
11. As soon as he began to reign and was seated on the throne, he killed off Baasha's whole family. He did not spare a single male, whether relative or friend.
12. So Zimri destroyed the whole family of Baasha, in accordance with the word of the LORD spoken against Baasha through the prophet Jehu--
13. because of all the sins Baasha and his son Elah had committed and had caused Israel to commit, so that they provoked the LORD, the God of Israel, to anger by their worthless idols.
14. As for the other events of Elah's reign, and all he did, are they not written in the book of the annals of the kings of Israel?
15. In the twenty-seventh year of Asa king of Judah, Zimri reigned in Tirzah seven days. The army was encamped near Gibbethon, a Philistine town.
16. When the Israelites in the camp heard that Zimri had plotted against the king and murdered him, they proclaimed Omri, the commander of the army, king over Israel that very day there in the camp.
17. Then Omri and all the Israelites with him withdrew from Gibbethon and laid siege to Tirzah.
...
23. In the thirty-first year of Asa king of Judah, Omri became king of Israel, and he reigned twelve years, six of them in Tirzah.
2 Kings 15:14-16:
14. Then Menahem son of Gadi went from Tirzah up to Samaria. He attacked Shallum son of Jabesh in Samaria, assassinated him and succeeded him as king.
15. The other events of Shallum's reign, and the conspiracy he led, are written in the book of the annals of the kings of Israel.
16. At that time Menahem, starting out from Tirzah, attacked Tiphsah and everyone in the city and its vicinity, because they refused to open their gates. He sacked Tiphsah and ripped open all the pregnant women.
Tirzah was last mentioned in Song of Solomon 6:4 where it either proclaimed the town had the beauty of Zelophehad's daughter or the city itself was nicely landscaped.