Using the word ‘bowdlerize’ gives a misleading impression, that only a very few Bibles retain an English rendition of the Divine Name; that the vast majority have expunged this word, that is, erased and omitted it from the Bible. If that was the case, then the Authorised Version and very many more recent translations would have failed to include the Tetragram at all, yet they have it in several places in the Hebrew scriptures, the most common places being Exodus 6:3 and Psalm 83:18. It is also the case that many old hymns have God’s name pronounced as Jehovah in some verses. Many times in church sermons I have heard God addressed as Jehovah when the Covenant God of Israel is being referred to. Given that many English translations retain Jehovah in a few places, it is misleading to say they have bowdlerized that word.
Now, it is undeniably true that the Tetragram was initially written 6,961 times in the ancient Hebrew scriptures (including 134 times where the Masoretic text shows that ancient copyists called Sopherim had changed the primitive Hebrew text to read ‘Adho.nay’ or ‘Elo.him’ instead of Yehowah’.) Yet Jewish believers themselves began to ‘lose’ the use of the Divine Name during and after their many years in captivity commencing particularly after the third Babylonian deportation of Judah in 586 B.C. Colonies of Jews were established in various areas of the Mediterranean world. Alexandria (Egypt) became an important center for expatriate Jews – a leading center of learning and Greek culture until it was conquered by Rome. Gradually, many Jews lost their ability to read and understand the Hebrew scriptures. Thus, around 280 B.C. a group of Hebrew scholars began translating the Hebrew Scriptures into Greek. The translation became known as ‘the Seventy’ (LXX) with a Latin name of the Septuagint.
An important point about this translation into Greek was that the Divine Name was rendered as YHWH in some Septuagint versions. Although many manuscripts of the Septuagint are available today that contain the word Kyrios [LORD] rather than the Tetragram, a discovery in Cairo of Aquila’s Greek text clearly shows the four Hebrew letters of the Tetragram. However, his translation was done during the second century C.E., so was not available to Jesus or the Apostles. Yet not all versions of the Septuagint retained the Tetragram, so eventually the divine name written in Hebrew letters was not understood any more.
Thus the way in which the Divine Name became less and less common was a process that started before 280 B.C. and continued until, by the time the Christian church was well established, the Tetragram was not understood by the majority of scripture readers. You need to go back centuries to discover this gradual reduction in use of the Tetragram in scripture translations. Nevertheless, it should be used nearly 7,000 times in the Hebrew scriptures, although a problem preventing that is not knowing an accurate word to translate it with, given that the vowel points remain missing. Rather than guess, (perhaps wrongly) many prefer to use the respectful LORD in the Hebrew scriptures. Erring on the side of caution is no bad thing when dealing with holy scripture. For example, given that the letter ‘J’ was not introduced into the English alphabet until the early 15th century A.D., ‘Jehovah’ is not the best attempt. I would personally be happy to see Yahweh written nearly 7,000 times in English translations of the Hebrew text, but I do not have a problem with ones that have LORD, because when capitalised, we all know that it refers to the one true God, the Creator.
Finally, when you say, “Jews do write the name in their holy texts” it needs to be pointed out that they still do not pronounce it.
Source: The Divine Name in the New World Translation, released for worldwide internet distribution in 2001 with no copyright. http://www.tetragrammaton.org