It's actually a kind of false friend or pun. The Latin Hibernia, first attested by Caesar, is derived from the archaic Irish Iweriu/Iveriu (possibly through the Greek Ierne), which is the earliest from of the modern Irish Eire. The Romans must have noticed how similar it sounded to 'land of winter' and, viewing Ireland as a comparatively cold country, just went with it. Ironically, Iweriu seems to have originally meant something like 'fat/fertile land'. Classical authors disagreed on how they imagined the Irish climate; Stabo called it 'a wretched place to live because of the cold', Pomponius Mela described it as unfit for grain but well-suited for livestock, and Tacitus claimed that its climate differed little from Britain.

Philip Freeman (2001), Ireland and the Classical World