You are correct, Fulltimestudent, with an additional "caveat," as you put it.
It is actually an act of naïveté that some non-Jews and especially Christians make in reference to Jewish religion and worship. Our religious practices and theology have never, ever been static. They not only changed under Hellenistic influence, as you mention, but in every era, with the winds of every political change.
Jews acknowledge a fact that is often disturbingly unamusing to the likes of Jehovah's Witnesses, namely that there was never a truly "pure" form of Judaism. It has never been "one original thing" (even if you read through the Hebrew Bible, which many JWs never have). Christians especially like to think that Judaism only changed with the Second Temple era and mistakenly draw Jesus as a "restorer" of "true" Jewish practice and thought (in reality, he was as much a product of the times as were the Pharisees). Political intrigue and changes to the map of history have always influenced Jewish theology, and it has bent for all types or reasons (not merely survival) with each passing century up to and after Jesus.
It is even a fundamental element to Jewish practice that Judaism never stays aloof and disconnected from the changing world around it. Except for small groups of fundamentalist Jews, the universal tenet of tikkun olam makes this impossible. The acknowledgement of this need for "staying in touch" and changing with the times does not come from many religious groups, like the JWs, who rely on a fictional retelling of Jewish history to make their house-of-card theology work.
As for the Name, part of the reason that it is not used to the extent that God remains essentially "nameless" is that the Jewish concept of "God" is very unlike the Christian and Muslim concept (not to mention the Watchtower brand of "God"). It is actually closer to atheism than the Christian concept of theism.
For Jews, all gods and all religions are false. There is no such thing as a god. Deities are fake. All of them are. The "God" of the Jews is what we recognize as the "Great Cause" and "Ultimate Purpose" of all. What or who is this, we don't know. Can it be truly understood or defined? No, not in Jewish thought.
But since the universe is here, the concept is that we are thus witnessing an "effect." The universe and world we live in is the effect produced by a "cause." This "cause" is what the Abrahamic God is. It is not "god" in the pagan or heathen view. It does not require belief anymore than the "effect" we witness does. The Great Cause of everything is the only thing that can be "God" in the sense that humans can grasp. It also, according to Jews, remains a mystery, much like agnostics acknowledge.
So it is very different from "God" taught in Sunday schools and Watchtower studies. YHWH is the "un-God," if you can grasp my meaning. That is why Jews can be atheist and still pray and worship. The two are not against one another in Judaism.
This makes the Name ineffable. We don't even recognize the pronunciation "Yahweh" in Judaism because it is as invented as the Catholic "Jehovah." It doesn't sound anything like anything in Hebrew. There's nothing like it. We only use "Yahweh" in discussions like this with Christians or those exposed to Christian thought, but the sound and name mean nothing. We don't recognize it as being the same as the YOHD HE VAV HE of HaShem. So there was never anything for Christianity to inherit when it came to a name's pronunciation. "Names" are not the sounds they make in Jewish culture, they are the person and their attributes.
But as one person said: "What do you Jews know about God or the Bible?" Until people listen and learn from the Jews about their God, they will never fully grasp the concepts so many of them hold dear (like Christianity). We Jews are always wrong, and the Gentile Christians and their "scholars" always know better. (Can I hear an "Amen!" from the Governing Body?) Sigh.