According to "Iranian Elements in the Georgian Language" written by Thea Chkeidze, Givi is one of the many Georgian names that originated from the 10th-century epic poem "Shahnameh" written by the Persian poet Ferdowsi:- https://www.cais-soas.com/CAIS/Culture/iranian_elements_georgian.htm (in English)She states that Givi comes from the Persian name Gev, which she writes as Gêv. [noted -ed]I went to see if there was indeed such a character in the "Shahnameh", and yes, there is:- https://en.wikipedia.org/wiki/Giv_(Shahnameh) (in English)He was the son of Goudarz and the son-in-law of the hero Rostam via his marriage to the latter's daughter Banu Goshasp.Note that the name Giv was not specially created for the "Shahnameh": it already existed before Ferdowsi wrote his epic poem:- https://en.wikipedia.org/wiki/Goudarz#Historical_Goudarz (in English) - https://en.wikipedia.org/wiki/Gotarzes_II_of_Parthia#Origins (in English; writes the name as Gev)You might also want to see the entry for Gave/Gev at http://www.avesta.org/znames.htm#parsi (in English).Also, my apologies for my previous comment from April 2019: I had misinterpreted the sources and it turns out that Giuna is actually the diminutive of Givi (i.e. the opposite of what I said applies!).
Sources: https://www.names.org/n/givi/about
https://forebears.io/x/forenames/givi