🔼The name Gideoni in the Bible
There's only one man named Gideoni in the Bible, but we only know about him because he was the father of Abidan, a leader among the Benjaminites. In Numbers 10:24 our name is spelled גדעוני, which shows that the letter נ (nun) is probably a remnant of the familiar ון extension, and that the name Gideoni is closely related to the name Gideon.
🔼Etymology of the name Gideoni
The name Gideoni comes from the root-verb גדע (gada'), meaning to hew down or cut off:
The letter י (yod) upon which our name ends may either form a possessive: my Gideon, or it makes Gideon into an adjective: Gideon-ish or from Gideon. It may also be a remnant of יה (Yah) = יהו (Yahu) = יו (Yu), which in turn are abbreviated forms of the Tetragrammaton יהוה, YHWH, or Yahweh.
For a meaning of the name Gideoni, NOBSE Study Bible Name List reads A Cutting Down. Jones' Dictionary of Old Testament Proper Names proposes Feller. BDB Theological Dictionary doesn't translate this name but does list it under the root גדע.