Yes, the abbreviated "Yah" can been seen in the Hebrew word "הללויה" but it the NT this is written in Greek (ἁλληλουϊά
and it is not something that a Greek reader would see as the name YHWH any more that English readers see the name YHWH in Halleluyah.
Of course it was in written in Greek letters as all text of manuscripts used for translation of the new testament are. It is presumption to say the early Greek readers among believers would not know the name of God occurring in such writing.
Even English speakers that have been taught that Halleluyah means "praise the Lord" often still don't understand why.
It is unfortunately the case so many English speaking believers (and I do mean them as believers) do not know or recognize the name of Yahweh. For this I refer to Exodus 3 where Yahweh (designated "the LORD" in many translations) says "This
is My name forever, and this
is My memorial to all generations", for it not to be neglected among all scriptures, with all scriptures for us to learn from.
None of this really matters because the NT authors were not inspired to put the tetragramaton into the text of the NT and neither should we.
This argument if true would then apply to putting "the LORD" with the capitals, when it is placed for where the name is meant, also in the new testament, this is also done. But the truth is that if any old testament scriptures are not written into the new testament, it does not mean all of that should be disregarded. I am not thinking of the exact four letters (the tetragrammaton) being used in writing in our language, but there is wide understanding that the ancient writing is representing what we say with the name of Yahweh as it is managed in our language. That or what form can be known as recognizing the name he revealed for us is appropriate, leaving it to be forgotten when it is known is not, according to what he said.
This is speaking on appropriate response to what God says, not speaking of condemnation or questioning anyone's salvation, as obedience to him comes from salvation, not salvation coming from obedience.