🔼The name Tibni in the Bible
There is only one Tibni in the Bible and although he apparently made quite an impact on Israel, he's only mentioned in one two-verse context.
In the third decade of the reign of king Asa, the great-grandson of Solomon, king of Judah, things went sour for the royalty of the northern kingdom of Israel. First king Elah was murdered by the usurping military commander Zimri. After seven days of his reign, the disgruntled people of Israel made Zimri's commander-colleague Omri king and when he marched upon the palace in Tirzah, Zimri burned it down with him in it.
But when Omri wanted to take the throne, another group of disgruntled Israelites had gathered behind yet another aspiring king-candidate: Tibni, son of Ginath. After a barely mentioned civil war that lasted from the twenty-seventh to the thirty-first year of king Asa of Judah, Tibni died from undisclosed causes, and Omri became king (1 Kings 16:21-22).
Omri may not be one of the most proverbially known kings of Israel, but he was the one who bought Samaria from Shemer and made it the capital of Israel. After his death, Omri's more notorious son Ahab took the throne.
🔼Etymology of the name Tibni
The name Tibni looks like it comes from the noun תבן (teben), meaning straw, or else the verb בנה (bana), meaning to build:
The letter י (yod) upon which our name ends, may either create an adjective (straw-like), a possessive form (my building), or may be a remnant of יה (Yah), which in turn is an abbreviated form of the Tetragrammaton יהוה, YHWH, or Yahweh.
For a meaning of the name Tibni, NOBSE Study Bible Name List appears to go with the verb בין (bin), meaning to discern and translates it with a dubious Intelligent.
Alfred Jones (Dictionary of Old Testament Proper Names) derives our name from the verb בנה (bana) and sees in the final yod a remnant of the Tetragrammaton, and translates our name with Building Of The Lord.
BDB Theological Dictionary does not offer an interpretation of our name but does list it under the noun תבן (teben), although this may be due to BDB simply following the alphabet and not to any suggested etymological kinship. Still, a Hebrew audience would probably be less impressed with the technical details of linguistics and recognize without further considerations the obvious similarity between our name, the noun תבן (teben) meaning straw and the verb בנה (bana), meaning to build.