🔼The name Temeni in the Bible
The name Temeni occurs only once in the Bible, although this name is spelled the same (and pronounced slightly different) as the ethnonym Temanite.
🔼Etymology of the name Temeni
The name Teman appears to be constructed from the noun תימן (teman), meaning south, from the root ימן:
The letter י (yod) upon which our name ends, may either create an adjective (southern), a possessive form (my south), or may 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 Temeni, NOBSE Study Bible Name List appears to go with the same Arabic connection that explains the name Imnah. Apparently, in Arabic the root ימן exists as well but with a primary meaning of being prosperous. NOBSE sees Temeni as a proper adjective and reads Fortunate.
Alfred Jones (Dictionary of Old Testament Proper Names) doesn't treat Temeni separately but refers to this name in his article on the name Teman. He deems Temeni "different" and "derived from a place unknown". Jones translates the name Teman with Southern Quarter, and seems to regards Temeni as an ethnonym with the same meaning as Temanite. We may assume that he would translate Temeni as One From The Southern Quarter.
BDB Theological Dictionary doesn't interpret this name but does list it under the root ימן.