Patronymically from Yether; a Jithrite or descendant of Jether -- Ithrite.
see HEBREW Yether
H3505. Yithri
יִתְרִי adjective, of a people, always with article הַיִּתְרִי 2 Samuel 23:38, ᵐ5 Αιθειραιος, etc.; 23:38, ᵐ5 Εθθεναιος, ᵐ5L Ιεθεμ; read perhaps הַיַּתִּירִי Th Klo Kit Bu; = 1 Chronicles 11:40 (twice in verse), ᵐ5 Ηθηρει, Ιεθ(ε)ρι, etc.; collective 2:53, ᵐ5 Αιθαλειμ, ᵐ5L Εθρι.