Sorry I posted 6 years late...
There are no greek manuscripts of the new testament that date to the original period of the 1st century. Any manuscript that contains the Tetragramaton would date centuries later. To use the LXX or Septuagint as the basis for reinserting the "name" into the new testament is not supported by the majority of scholars. Why? Because they are two separate and distinct works for one, written by two different groups of people with a different perspective and purpose.
Some would state that to insert the "name" into the New Testament, except only in cases where it may appear in the LXX as a direct quote is a cause for concern.
SOP