Discrepancy between Yahweh (Christian Bibles) and Eh-yeh (Torah) I am currently working on a religious drama and outsmarted myself. I come to you for help.

Growing up Jewish, I did not hear the term Yahweh until I was 14 in Western Civilization. "Well, you know, right? It's, you know, God." And my reply, "I have no idea what you're talking about, and seriously, there isn't even a w in Hebrew so try again." Nor in Ancient Greek! Although, some would say the Hebrew letter vav can behave like a w.

Next, my Torah portion included Exodus 3:14 (and I gotta tell you, reading off an animal skin scroll is cool!). It says Eh-yeh asher Eh-yeh. Even among Jews, there is some controversy because of limitations within Hebrew of future tense. However, "I shall be what I shall be" is without fault as an English translation of the Hebrew. Certainly the Christian Bible "I am who [what] I am" is a very different statement. The Torah has been meticulously transcribed letter by letter for 2600 years 

So I asked a (Conservative) rabbi. We agreed the line from Exodus 3:14 contained neither a Yah nor a weh. "So, Rabbi, where does this word come from?" She says, "Well it really has nothing to do with Exodus 3:14. Here read this." And I read, "Barukh atah Adonai--" 

"You can stop there," she says. "The third word does not state 'Adonai.' Why do you say that?" And my response is "Because that [what I read] is how we spell our Lord's name on paper--probably to prevent us from being insulting." And she says "And what does it actually read?" My Hebrew is not so great but I manage "Yeh-vah?" She says, "That's the best I can do."

Although I might benefit from seeing a Protestant minister, I wound up with a visit at a nearby Catholic Church. Although we came to no further conclusion on the matter, we agreed that Yeshua was an awfully nice Hebrew name.

I've read quite a bit over the years on the subject. Most of the commentary is either too mystical or too one-sided to be useful to my project or me.

Specifically, how did "Yahweh" become a word of such prominence in Western literature and lexicon?

I've redacted the latter part of my question, and thank you for your information thus far.

For clarification, I'll add: YHVH, or whatever you want to call it, is little more than a placeholder in modern Hebrew prayers; it is simply not said, and has been further redacted to YY. I've seen it a million times, but I just say Lord ("Adonai"). The idea that the placeholder held any real significance was lost on me until much later in life. I do not know what was spoken in biblical times, but that doesn't matter. The discussion of Jehovah below is helpful, but as long as I'm still open for business ...

Edit: I recently asked an Orthodox rabbi. Orthodox Judaism tends to be more mystical, if you will (Chabad.org). The response: "It is actually one of many names for the Divine. ... It was not used in general prayers during the times of the Temple [Kings]. ... It is unknown what was spoken during the time of Moses."
Here is a basic answer:

In Exodus 3:14, אֶֽהְיֶה (eh-yeh, a form of the Hebrew verb "to be") is used as part of what today would be considered a folk etymology of the most sacred Hebrew name of God, called the "Tetragrammaton": יהוה as it appears in the original unpointed (no vowels) Hebrew manuscripts. Eh-yeh is not itself the commonly used name for God in the Hebrew Bible. It is used in Exodus 3:14 only to give meaning to the Tetragrammaton, which is the common, but very sacred, name for the God of the ancient Hebrews. The force and basic meaning of the etymology in Exodus 3:14 is that God is called יהוה from the verb "to be": God is the one who is or who, in more modern philosophical terms, is the ultimate reality and the self-existing (uncreated) being.

In the Hebrew Bible, this name is usually pointed (given vowels) as: יְהֹוָה or Yĕhovah in English pronunciation. It is translated as "Jehovah" in some English Bibles.

However, that pronunciation is not based on how it was originally pronounced at the time the Hebrew Bible was written. As the Rabbi pointed out to you, when יְהֹוָה appears in the Hebrew Bible, Jews regularly read it as "Adonai" instead. The Hebrew for Adonai is אֲדֹנָי. And that is where the vowel pointings commonly used for יְהֹוָה in today's Hebrew Bibles come from (with a slight variation due to how various Hebrew letter combinations take vowels).

In other words, the word that is traditionally transliterated into English as "Jehovah" (or as "LORD" in small caps in the KJV and other traditional English bibles) is actually a combination of the consonants from the Tetragrammaton יהוה and the vowels from the Hebrew word "Adonai," which means "Lord."

You see, the Tetragrammaton was, and still is today, considered too sacred to be pronounced by most religious Jews. So when they encounter it in the Bible, they say "Adonai" instead. And the vowels, which were added later, reflect that substitution of "Adonai" for the Tetragrammaton when reading.

Because of this tradition of not pronouncing the Tetragrammaton, which stretches back over two thousand years, we do not know for sure how it was originally pronounced. "Yahweh" is what most scholars now think was the original pronunciation of the Tetragrammaton—which is why that pronunciation is commonly used in scholarly circles and among some groups of Christians.