I think a cursory reading of the New Testament would give us a clear picture of the glaring lack of emphasis on the Divine Name, YHWH, and a huge emphasis on the name of Jesus, which contains the divine name anyway, in its meaning.
1 Thessalonians, for example, even in the NWT mentions Jehovah 3 times and Jesus or Christ 18 times. Christians were named Christians for a reason--they bore witness to the name of Jesus. The Israelites had obviously failed in bearing witness to YHWH, but now the chance was being given for God to be viewed as the God of everyone, not just Israel, and Jesus was the way to do that. This emphasis on the divine name is a bit of a false foundation on which to measure true Christians by in itself, as the original true Christians were as obsessed with the name Jesus as Jehovah's Witnesses are with the name Jehovah.
Reading the appendix in Jason David BeDuhn's book (Truth in Translation) about the NWT's improper use of Jehovah in the New Testament might be insightful on this.
-sd-7