The name which He gave to Moses was (in Hebrew) "Ehyeh Asher Ehyeh", or "I am that I am" or "I will be what I will be".
Throughout the Old Testament the most prolific name, indeed that which is regarded as the Sacred Name is the Tetragrammaton ("the four letters") Yod Hah Vav Hah (YHVH or YHWH).
By Jesus' time Jewish tradition considered it inappropriate to speak or write the divine name carelessly, and so almost exclusively it was the high priest alone who spoke the name and only when he entered into the Holy of Holies on the Day of Atonement. The idea was that God's name was to be absolutely revered, and to be treated with absolute delicacy and respect. This tradition has preserved into the present day which is why if you see articles or blogs or even forum posts online many Jews will write G-d, G_d, or Gd instead of "God" because all things that have to do with God are to be treated with respect (in this case it's a precaution, because someone could print it out and then, say, throw the paper away which would be disrespectful). It's also why Jews often say "HaShem", HaShem is Hebrew for "the Name".
In the middle ages Jewish scholars came up with a system of pronunciation marks known as niqqud. Hebrew contains no written vowels, and thus right pronunciation is largely the result of knowing the language intimately, as Jewish scholars aimed to improve literacy in Hebrew among the Jewish diaspora they wanted more Jews to be able to read and right in Hebrew, especially to be able to read Torah. Niqqud effectively took the place of written vowels.
As far back as the Septuagint, centuries before Jesus, it was common to say "adonai" (lord) instead of the Name itself. The Septuagint, for example, renders the Divine Name as "kurios", that is, "lord". The New Testament, as it quotes the Septuagint, retains "kurios" where "YHVH" appears in the Hebrew text of the Old Testament.
When the Masoretes, the previously mentioned medieval scholars and scribes, used niqqud to aid in pronunciation of written Hebrew they used the niqqud for Adonai where YHVH was in the text. This was done so that the reader would know to say Adonai.
Christian scholars in late medieval Western Europe didn't seem to know this, and so when they transcribed the Hebrew into Latin characters it came out as Iehovah/Iahovah.
To give an idea of how this happened consider:
The Hebrew word Adonai contains only four consonants, Aleph, Dalet, Nun, and Yod or 'DNY, the niqqud vowel markings make it something like 'aDoNaY. The letters for the Tetragrammaton are YHVH, add the vowels and you get YaHoVaH or YeHoVaH, or in Latin Iehovah.
The 'J' is the result of consonantal 'i' becoming a 'j' in late medieval Latin. In English the 'j' took on a hard sound as in jam, jet, etc. And hence "Jehovah". A bizarre accident of linguistics that's hung around for a really long time.
So then how do we actually pronounce YHVH? Truth is we simply don't know. The pronunciation has long been lost in Judaism, though the Samaritans have continued to preserve the Name to this day. In Samaritan Hebrew it is pronounced as either Yahwe or Yahwa. Early Greek writers, such as the Church Fathers, transcribed the pronunciation as Iao.
Personally I call Him Father, Son, and Holy Spirit; and know the Son as Jesus Christ, our Lord.
-CryptoLutheran
