I’ve been thinking about this question posed above or in another thread: if the divine name was originally in the NT then why didn’t Origen mention it was in the NT the same way he mentioned that the most accurate copies of the LXX contained the divine name? I think the reason for that may be the fact that when Christians stopped using copies of the LXX that contained the divine name Jews nevertheless continued to use copies of the LXX and other Greek versions of the OT that contained the divine name. So the reason there were still copies of the LXX around with the divine name for Origen to find is because Jews were still using them. When it comes to the NT obviously Jews didn’t preserve copies of the NT as they did the OT in Greek, so when Christians stopped using copies of the NT with the divine name they fell into disuse altogether. Remember that Origen sourced the best manuscripts of the LXX he could find from Jews. He couldn’t do the same with the NT. Another thing to remember is that the earliest and most accurate copies of the LXX that Origen could find contained the divine name in the form of the tetragrammaton, whereas we know that the early LXX used the form the divine name transliterated into the Greek Yaho. Origen doesn’t mention finding any of those, even though we know that they existed and that copies of the LXX with Yaho are probably the closest analogy to how the early NT would have handled the divine name.
As for the early Christian use of the divine name transliterated into the form Yaho, we have the testimony of the early onomastica name lists that Christian scribes preserved for centuries into the common era. These strongly indicate that at an early stage of their transmission Christians used copies of the LXX and NT with the divine name transliterated into the Greek form Yaho. It is difficult to account the for the use of Yaho in the onomastica otherwise.
On top of which George Howard’s basic point still stands: the contemporary manuscript evidence indicates that Jews in the first century used the divine name in their texts and it is reasonable to think NT authors probably followed contemporary practice. The fact that the NT text contains so many variants around loci with the divine name corroborates this argument as Earnest has explained above.