What are the arguments for and against YHWH/Yahweh/Jehovah is the name of God forever?

Exodus 3:15 Literal Standard Version

And God says again to Moses, “Thus you say to the sons of Israel: YHWH, God of your fathers, God of Abraham, God of Isaac, and God of Jacob, has sent me to you; this [is] My Name for all time, and this [is] My memorial, to generation [and] generation.

Young’s Literal Translation

And God saith again unto Moses, ‘Thus dost thou say unto the sons of Israel, Jehovah, God of your fathers, God of Abraham, God of Isaac, and God of Jacob, hath sent me unto you; this is My name — to the age, and this My memorial, to generation — generation

Aramaic Bible in Plain English

And God said again to Moshe: “In this way speak to the children of Israel: ‘LORD JEHOVAH, the God of your fathers, the God of Abraham, the God of Isaac, the God of Yaquuv has sent me unto you’; this is my Name to eternity and this is my memorial to a generation of generations.

If forever means eternity, is God’s name really not in the New Testament? If it is not in the NT, then what does that say about YHWH being God’s name forever?

What are the arguments for and against the Father is the God/YHWH/Yahweh/Jehovah spoken of in this verse?