A long time ago, I was reading in Exodus and came to 3:15, which speaks of the Lord's Name and also His memorial, and the thought occurred to me - Most people (including myself up to this point) probably probably see the Lord being God to the successive list of Abraham, Isaac and Jacob as a memorial of His faithfulness to His people over time. I know that in many cultures, including the Hebrew culture, a person's name stands for their essence and character. But a memorial seems to be more focused on something a person has done. As I meditated on this verse, Psalm 2 came to mind and I saw a possible connection between the meaning of the names Abraham, Isaac, and Jacob to something that the Lord will do which will serve as His memorial. The Lord will become the "Father of Many Nations" (the nations who rage and plot vain things Ps2:1) when He "Laughs" (Ps. 2:4) and "Supplants" the king that the rebellious nations have tried to set up in opposition to Him. (Yet I have set MY King on My holy hill of Zion Ps. 2:6) Any thoughts on this as a possibility?
Yes, I can see a general commonality between Psalm 2 and Exodus 3:15. While I don’t believe the Psalmist is directly alluding to Exodus 3, I can see some commonality. In both sections of scripture there are common themes: nations raging against God (Egypt in Exodus), the concept of inheritance and in trusting in the Son of God by faith.
In Psalm 2:1-3, the nations rage against the Lord and His anointed. In Exodus 3, the greatest example of that truth is the nation of Egypt and Pharaoh’s rebellion against God and His anointed Moses.
Why do the heathen rage, and the people imagine a vain thing? 2 The kings of the earth set themselves, and the rulers take counsel together, against the Lord, and against his anointed, saying, 3 Let us break their bands asunder, and cast away their cords from us.
In Psalm 2:9, God then supplies correction to the nation of Egypt through the 10 plagues in effect, smashing Egypt with a rod of iron.
Thou shalt break them with a rod of iron; thou shalt dash them in pieces like a potter's vessel.
However, the greatest area of commonality between Exodus 3 and Psalm 2, I believe, can be seen in Psalm 2 verses 8 and 12 where the Psalmist introduces the ideas of inheritance and faith.
8 Ask of me, and I shall give thee the heathen for thine inheritance, and the uttermost parts of the earth for thy possession.
12 Kiss the Son, lest he be angry, and ye perish from the way, when his wrath is kindled but a little. Blessed are all they that put their trust in him.
In Exodus 3:15-17, scripture deals with the subject of inheritance stating that the God of Abraham, Isaac and Jacob will give the land of Caanan to the Israelites. In verse 17, we see God repeating the promise of inheritance to Abraham's descendants from Genesis 12:7. Note also the reference to the Gentile nations as part of the inheritance.
15 And God said moreover unto Moses, Thus shalt thou say unto the children of Israel, the Lord God of your fathers, the God of Abraham, the God of Isaac, and the God of Jacob, hath sent me unto you: this is my name for ever, and this is my memorial unto all generations. 16 Go, and gather the elders of Israel together, and say unto them, The Lord God of your fathers, the God of Abraham, of Isaac, and of Jacob, appeared unto me, saying, I have surely visited you, and seen that which is done to you in Egypt: 17 And I have said, I will bring you up out of the affliction of Egypt unto the land of the Canaanites, and the Hittites, and the Amorites, and the Perizzites, and the Hivites, and the Jebusites, unto a land flowing with milk and honey.
Now we know from the Book of Hebrews that the inheritance of the physical land of Israel is not the inheritance the God was speaking about. The land is a metaphor for salvation through Jesus Christ and all those who believe by faith are counted as part of the promise of inheritance that God made to Abraham. Our real inheritance is heaven.
Hebrews 11: 13 These all died in faith, not having received the promises, but having seen them afar off, and were persuaded of them, and embraced them, and confessed that they were strangers and pilgrims on the earth. 14 For they that say such things declare plainly that they seek a country. 15 And truly, if they had been mindful of that country from whence they came out, they might have had opportunity to have returned. 16 But now they desire a better country, that is, an heavenly: wherefore God is not ashamed to be called their God: for he hath prepared for them a city.
As you stated in your question, this is most significant, for God stated that “this name” will be His name forever; God will forever be known as the God of Abraham, Isaac and Jacob. This name connotes family line and inheritance.
This is the story of the gospel. For entrance into the family of God is not due to any works of righteousness that we can do but only through the grace and mercy of God. This family inheritance was promised to Abraham and all those who would follow by faith. The Galatians chapter 3 sums it up quite well.
16 Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many; but as of one, And to thy seed, which is Christ. 17 And this I say, that the covenant, that was confirmed before of God in Christ, the law, which was four hundred and thirty years after, cannot disannul, that it should make the promise of none effect. 18 For if the inheritance be of the law, it is no more of promise: but God gave it to Abraham by promise. 19 Wherefore then serveth the law? It was added because of transgressions, till the seed should come to whom the promise was made; and it was ordained by angels in the hand of a mediator. 20 Now a mediator is not a mediator of one, but God is one. 21 Is the law then against the promises of God? God forbid: for if there had been a law given which could have given life, verily righteousness should have been by the law. 22 But the scripture hath concluded all under sin, that the promise by faith of Jesus Christ might be given to them that believe. 23 But before faith came, we were kept under the law, shut up unto the faith which should afterwards be revealed. 24 Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith. 25 But after that faith is come, we are no longer under a schoolmaster. 26 For ye are all the children of God by faith in Christ Jesus. 27 For as many of you as have been baptized into Christ have put on Christ. 28 There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus. 29 And if ye be Christ's, then are ye Abraham's seed, and heirs according to the promise.
The bible 17 times calls God the God of Abraham, Isaac and Jacob. The bible never calls God the God of Moses; inheritance is always by promise and never by performance.
All scripture references KJV.