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YHWH
Almighty God, the Father
Isaiah 42:8 (TS2009)
I am YHWH, that is My Name, and My esteem I do not give to another, nor My praise to idols.

Hebrew reads from right to left. The Name of God as given in the Old Testament is Yod He Waw He according to the Hebrew Aleph-Bet. In the New Testament God's Son reveals God to be His Father. God's Name transliterated into English is YHWH. It is called the tetragrammaton which simply means the four letters. In Hebrew names have a meaning, they reveal something about the one who carries the name.
Ehyeh ašer ehyeh
Exodus 3:14-15 (TS2009)
And Elohim said to Mosheh, "I am that which I am." And He said, "Thus you shall say to the children of Yisra'el, 'I am has sent me to you.' " And Elohim said further to Mosheh, "Thus you are to say to the children of Yisra'el, 'YHWH Elohim of your fathers, the Elohim of Abraham, the Elohim of Yitshaq, and the Elohim of Ya'aqob, has sent me to you. This is My Name forever, and this is My remembrance to all generations.'

The Hebrew words given by God to Moses are "ehyeh ašer ehyeh". It is often translated as "I Am Who I Am". The root verb here is "lihyot" which means "to be"...
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Gramatically the future tense is the best translation of "ehyeh". The word "asher" is a relative pronoun which can mean: who, which, that. This means the phrase can be translated as I Will Be Who I Will Be or I Will Be What I Will Be. It is about existence and the future tense seems to reveal a prophetic value.
Yah
Psalms 113:1 (TS2009)
Praise Yah! Praise, O servants of YHWH, Praise the Name of YHWH!

King David addresses God with the Name "Yah". Yah is a short form of YHWH. It consists of Yod and He, the first two characters of His complete Name YHWH.
Revelation 19:1 (TS2009)
And after this I heard a loud voice of a great crowd in the heaven, saying, "Halleluyah! Deliverance and esteem and respect and power to YHWH our Elohim!

The only mention of God's Old Testament Name in the New Testament, besides the few literal quotes of the Old Testament, is in the Book of Revelation where the same expression is used as in Psalms. HalleluYah!
Abba, Father
Mark 14:36 (TS2009)
And He said, "Abba, Father, all is possible for You. Make this cup pass from Me. Yet not what I desire, but what You desire."

Galatians 4:6 (TS2009)
And because you are sons, Elohim has sent forth the Spirit of His Son into your hearts, crying, "Abba, Father!"

It is remarkable that the Hebrew Old Testament mentions the Name YHWH thousands of times while the New Testament barely mentions it, merely in those verses where the Hebrew Scriptures are quoted. Not surprisingly the Son of God addresses God as Father. Knowing that YHWH stands for existence and literally means I Will Be What I Will Be it makes sense to believe that this Name of God was fulfilled with the coming of His Son, the Messiah. The Messiah was the living proof of God's existence. The Messiah literally said I have come in My Father's Name... (John 5:43). He also said "He who has seen Me has seen the Father" (John 14:9). Since that time God is known as the Father to the followers of the Messiah, God's people. The Messiah also said he who receives Me receives Him who sent Me (Matthew 10:40). This doesn't mean that YHWH is no longer God's Name, it forever is (Exodus 3:15), but the Son of God has revealed that those who follow Him can call Him Father. He is a personal God who seeks a personal relation instead of a formal one (Romans 5). That's why His Son brought a renewed covenant in which the law is written on the heart or inwardly, not only in stone or outwardly (Jeremiah 31:33, Ezekiel 11:19-20, Ezekiel 36:26, Romans 2:14-15,29, Hebrews 10:16, 2 Corinthians 3:3).
The Aleph and the Taw
In the Hebrew interlinear of Genesis 1:1 of God's Word we see that one word is not translated. It consists of the letters Aleph and Taw. Now look what the Son of God says in God's Name in Revelation...

Revelation 1:1-2 (TS2009)
Revelation of YHWSO Messiah, which Elohim gave Him to show His servants what has to take place with speed. And He signified it by sending His messenger to His servant Yohanan, who bore witness to the Word of Elohim, and the witness of YHWSO Messiah — to all he saw.

Revelation 22:13 (TS2009)
I am the 'Aleph' and the 'Taw', the Beginning and the End, the First and the Last.

In the Greek interlinear of Revelation 22:13 we of course find the Greek letters "Alpha" and "Omega". The Aleph-Taw in the very first sentence of the first Book of the Old Testament signifies God. In the Revelation to John, which is generally understood to be the last Book of the New Testament, He reveals that He is the Aleph and the Taw. From beginning to end the Scriptures are the Word of God (Isaiah 41:4, Isaiah 46:10).
Pronunciation?
I found no evidence for the correct pronunciation of the Name YHWH. It has been lost with time and is currently unknown. If the correct pronunciation were important God would have preserved it. More important than the pronunciation is what His Name stands for, His character and reputation, and that He is the One Living True God who seeks to be our Father. God knows people's hearts and that is more important than how people pronounce words or names (1 Samuel 16:7, Luke 16:15-17).