There is no evidence that the name was ever used in the NT. The NT writers quoted from the Septuagint. The wording of NT's quotations from the OT makes this clear. The common Septuagint of the day did not use the divine name. It used "Adonai" (Lord). This is why the name does not exist in NT passages that quote from the OT. They were not quoting from the Hebrew scriptures. They were quoting from the Greek translation of the OT.
The evidence of the Tetragrammaton being used in the Septuagint is unconvincing. What I mean by that is that it does not appear that this was the norm in the first century. It seems likely that a few wealthy individuals who had a fixation for the divine name may have paid to have specialty copies containing the Tetragrammaton in Hebrew letters. But those are special cases - not the typical common septuagint that most persons used, and evidently not the Septuagint used by the writers of the NT. It is also possible that much older Septuagints customarily contained the divine name in Hebrew but this practice long ceased by the time the NT was written.
The total absence of NT manuscripts containing the divine name does not speak well for the idea that the name was originally in the NT. Were "apostate Christians" so thorough in their work that not a single manuscript with the divine name survived? That seems very unlikely considering that we have both OT manuscripts with the Tetragrammaton and ones with it replaced with Lord. Why aren't we seeing the same pattern with the much newer NT manuscripts?
The idea of the divine name originally being in the NT is nothing but wishful thinking born of a self-righteous, superstitious fixation with the word "Jehovah". The NT shows the Christians were not fixated with the divine name. They were fixated with the name of Jesus. They repeatedly referred to Christians as being witnesses of Jesus - not Jehovah's Witnesses.