The NT does not mention the Tetragrammaton itself, but Rev 4:8 mentions its meaning as revealed in Ex 3:14-15.
God said to Moses, "I AM WHO I AM"; and He said, "Thus you shall say
to the sons of Israel, 'I AM has sent me to you.'" God, furthermore,
said to Moses, "Thus you shall say to the sons of Israel, 'YHWH, the
God of your fathers, the God of Abraham, the God of Isaac, and the God
of Jacob, has sent me to you.' This is My name forever, and this is My
memorial-name to all generations.”
We have to take into account two properties of Hebrew verbs: stem and form.
A verb stem is an offshoot of the root that is used to indicate the properties of voice and aspect. The relevant stems here are:
- Qal stem: Simple action, active voice;
- Hifil stem: Causal action, active voice.
Hebrew has two main verb forms: the Perfect and the Imperfect. The perfect describes completed action whereas the imperfect describes actions or states which are incomplete, ongoing, habitual, or continual.
The Name revealed in Ex 3:14, "Ehyeh", is qal stem, first person, singular, imperfect form, of the verb "hyh", "to be". Therefore it means "I was", "I am", or "I will be", all in a continuing sense, depending on the context where it may be used. So if used by God in the first person, since God lives in eternity, which is not an infinite succession of moments but one moment of infinite fullness, it will be "I Am" (which is clear in Jn 8:58, when Jesus says "before Abraham was, I Am", and not "before Abraham was, I was").
The Name revealed in Ex 3:15, "YHWH", comes from "hwh", an earlier variant of the root "hyh", "to be". In contrast to "Ehyeh", it can have two possible meanings depending on its vocalization:
qal stem, third person, singular, imperfect form, if vocalized "YiHWeH", meaning "he was", "he is", or "he will be", all in a continuing sense, and depending on the context where it may be used. So if it is used by a creature, which exists in time, to refer to God, it would refer to all three meanings at the same time, as in the past God continually was, in the present God is, and in the future God will continually be: "He Was, Is and Will Be". Thus, in this case the Tetragrammaton is the same Name revealed in Ex 3:14 but pronounced by a creature, denoting God as He is in Himself: Absolute, Subsistent Being.
hifil stem, third person, singular, imperfect form, if vocalized "YaHWeH", meaning "He causes to be", or, more completely, "He was causing, causes and will cause to be". In this case, while the Name of Ex 3:14 denotes God as He is in Himself, the Name in Ex 3:15 denotes God as He is for us: the Creator.
Now, compare the first option with Rev 4:8:
And the four living creatures, each of them with six wings, are full
of eyes all around and within, and day and night they never cease to
say, “Holy, holy, holy, is the Lord God Almighty, Who Was and Is and
Is to Come!”