Google is not wrong, just inconsistent. The Greek transliteration (not the translation) of
גיהינה
was
γεένα
in the Septuagint, an early Greek translation of the Hebrew scriptures. At that time, this was not a legitimate word in the Greek language. I believe the second epsilon in the Greek is supposed to be aspirated (or at least preceded by a glottal stop), so the English transliteration (again, not the translation) would be gehenna, which happily also happens to be an approximate English transliteration of the Hebrew, which is probably good enough, since no one knows exactly how ancient Hebrew was originally pronounced anyhow.
Leaving out the aspiration, I think something like Gayna or Genna might be suggestive enough of Gehenna. (The Greek letter gamma (g) is always hard. It never has a j sound.)
By the way, the Septuagint (Greek) translation of the Hebrew Bible was done for the Jews of that day, not the Greeks. Only the Jewish scholars could read Hebrew. Most of the Jews spoke Greek. Hebrew became a forgotten language, which is why we don't know exactly how it was originally pronounced. (Hope I have my history right. It has been many years since I studied it.)
Okay, how about, then, an English translation of one of those, like Hinnom Valley. (Ge-Bene-Hinnom = "Valley of the Sons of Hinnom," in case that's good for anything.)
