The Old Testament name for God is YHWH, which has been translated as "Jehovah" in some English Bibles. "Yahweh" is probably a better rendering. When Jewish scholars around the 2nd century BC made a Greek translation of the Hebrew Scriptures (known as the "Septuagint," which is abbreviated "LXX"), they chose to use the word for "Lord" rather than the actual name of God, since there was a Jewish tradition at the time of not pronouncing the Name. The apostles, in writing the New Testament books, quoted freely from the LXX without ever making any bones about the fact that the divine Name had been "removed" from it. Apparently the fact that they regarded Jesus as having the "name above EVERY name" was more important to them than the correct rendering of YHWH.
Psalm 83:18 is a big deal only because it is one of the four places where the translators of the King James Bible broke from their usual custom of rendering YHWH as "Lord" and instead rendered it as "Jehovah." Nonetheless, there are over 6000 other places where the Hebrew manuscripts contain YHWH that could just as legitimately have been rendered "Jehovah," so Psalm 83:18 is nothing special in that regard. The JW's have just made a big deal of it because so many people own the King James Version and they could surprise people by getting them to open their own Bible and see that God's name is Jehovah. In the New Testament, the name of Jesus is the one that is important; the name of Jehovah is never directly mentioned, and the NT writers had no problem quoting the LXX using "Lord," when the actual Hebrew said YHWH. So the issue of the Name wasn't as important a matter as the JW's would have it.
By the way, this also means that it wasn't "the churches" that removed the name of Jehovah from the Bible, as the JW's would have you believe - it was the pre-Christian Jewish translators of the LXX, and the apostles tacitly endorsed that usage by quoting the LXX in their writings without objection.
