Briefly the WTS arguments are summarized:
1 The original LXX contained the Tetragammaton in Heb charcters
2 Most LXX scholars recognize this
3 Several ancient Heb manuscripts [called the "J" references] use the Tetragammaton
4 Jesus recognized the importance of Gods "name" [Matt 6:9, Jo 17:26]
Now the facts:
1 The WT's claim of the "original" LXX having the Tetragrammaton rests soley on the evidence of a Papyrus MS dated to the 1C BC called the Fouad 266. This set of fragments contains portions of the book of Deuteronomy, and in 49 places the Tetragammaton can clearly be seen in Hebrew characters among the Greek. It is sheer nonsense to conclude that because the Fouad 266 is one of the oldest of LXX MSS that it represents the original.
There is at least one other fragment of an LXX MS - found among the Dead Sea Scrolls, catalogued as 4Q LXX Lev [a] which in fact does not contain the Hebrew name. It uses "Kurios". Also dated to the 1CAD it may be older than the Fouad 266, by at least a generation.
It is impossible to determine what the "original" LXX said, because ever since its first publication in the 3C BC it was published in several "recensions" [editions which had an original syntax]. The only thing we can say for certain is that by the 1C AD when the NT was being written, several copies of the LXX were in circulation, of which one, representing the book of Dt, contained the Divine Name.
2 This is an exaggeration. Most scholars do not in fact recognize this. One scholar, Prof George Howard did, back in 1977 write an article for the Journal of Biblical Literature where he suggested that the NT writers may have had access to LXX MSS which contained the Divine Name, however, whether they then actually wrote the Tetragammaton down was not proved. He admitted his idea was only a "theory" and subject to scholarly debate.
The WTS however, not only concurred with Prof Howard's views, but made him say much more than what he actually did. They posited his "theory" as fact [See BRef pg 1564]
3 There is no Hebrew MSS of the NT available. The Hebrew texts that are being referred to by the WTS are in fact "translations" of printed texts [hence not hand-written MSS] of the NT dating from the 13th C at the earliest. Two problems arise from the use of the WTS using these "J" documents. Many of them are in fact based on the Erasmus RT NT text, which the WTS has rejected as being false. Evidently a corrupt NT text can preserve a better representation of the NT than many of the earliest Greek MSS. Secondly, many of these "J" references were published after the NWT was brought out!! For instance J 20 was published in 1963, J 22 in 1979, and J 23 in 1975.
4 It is true that Jesus proclaimed the "name" of God. But what name? The evidence cleary shows that the "name" Jesus proclaimed was "The Father" [capital "T" capital "F"] To suggest that The Father is only a title and not a "name" is facetious, to say the least, since even the WTS admits that the word "name" refers to one's position of authority.[ Compare the expression, "in the NAME of the Holy Spirit", and see "Insight" Vol 2 pg 464]
Hope tis helps
Cheers