To approach this question, historical context is required. In the beginning, God regarded Creation as "very good" (Gen 1:27-31). But when Adam and Eve disobeyed and introduced sin, they were removed from the presence of God and the Garden of Eden (Gen 3:22-24).

So God created man in his own image, in the image of God he created him; male and female he created them. And God blessed them. And God said to them, "Be fruitful and multiply and fill the earth and subdue it, and have dominion over the fish of the sea and over the birds of the heavens and over every living thing that moves on the earth." And God said, "Behold, I have given you every plant yielding seed that is on the face of all the earth, and every tree with seed in its fruit. You shall have them for food. And to every beast of the earth and to every bird of the heavens and to everything that creeps on the earth, everything that has the breath of life, I have given every green plant for food." And it was so. And God saw everything that he had made, and behold, it was very good. And there was evening and there was morning, the sixth day. (Gen 1:27-31)

Then the Lord God said, "Behold, the man has become like one of us in knowing good and evil. Now, lest he reach out his hand and take also of the tree of life and eat, and live forever—" therefore the Lord God sent him out from the garden of Eden to work the ground from which he was taken. He drove out the man, and at the east of the garden of Eden he placed the cherubim and a flaming sword that turned every way to guard the way to the tree of life. (Gen 3:22-24)

With His covenant with Abraham, God promises unilaterally and unconditionally to be God to Abraham and Abraham's descendants that share his faith (a trust and obedience to His word). The apostle Paul provides clarity on who a descendant of Abraham is when explaining the transition from faith in the Old to faith in the New Covenant (Rom 4:16-17).

And I will establish my covenant between me and you and your offspring after you throughout their generations for an everlasting covenant, to be God to you and to your offspring after you. And I will give to you and to your offspring after you the land of your sojournings, all the land of Canaan, for an everlasting possession, and I will be their God." (Gen 17:7-8)

That is why it depends on faith, in order that the promise may rest on grace and be guaranteed to all his offspring—not only to the adherent of the law but also to the one who shares the faith of Abraham, who is the father of us all, as it is written, "I have made you the father of many nations"—in the presence of the God in whom he believed, who gives life to the dead and calls into existence the things that do not exist. (Rom 4:16-17)

God's choice of being God to a person includes knowing the name of the one who has faith in Him. Observe carefully that Moses asked God to show him His ways so that he could know Him and continue to find favor in His eyes. Moses recognized the significance of the all powerful living God choosing to be God to an insignificant being like Moses.

Then Moses answered, "But behold, they will not believe me or listen to my voice, for they will say, 'The Lord did not appear to you.'" The Lord said to him, "What is that in your hand?" He said, "A staff." And he said, "Throw it on the ground." So he threw it on the ground, and it became a serpent, and Moses ran from it. But the Lord said to Moses, "Put out your hand and catch it by the tail"—so he put out his hand and caught it, and it became a staff in his hand— "that they may believe that the Lord, the God of their fathers, the God of Abraham, the God of Isaac, and the God of Jacob, has appeared to you." (Ex 4:1-5)

Moses said to the Lord, "See, you say to me, 'Bring up this people,' but you have not let me know whom you will send with me. Yet you have said, 'I know you by name, and you have also found favor in my sight.' Now therefore, if I have found favor in your sight, please show me now your ways, that I may know you in order to find favor in your sight. Consider too that this nation is your people." (Ex 33:12-13)

When revealing the conditional Mosaic Covenant, God reiterates His promise to Abraham to be his God; however, observe that His choice of a person is conditioned on their obedience to His word (Ex 19:4-6), and according to Moses, to learn God's ways is the way to know God. To be God to a faithful human being meant that God would be present with him.

I will dwell among the people of Israel and will be their God. And they shall know that I am the Lord their God, who brought them out of the land of Egypt that I might dwell among them. I am the Lord their God. (Ex 29:45-46)

And I will walk among you and will be your God, and you shall be my people. I am the Lord your God, who brought you out of the land of Egypt, that you should not be their slaves. And I have broken the bars of your yoke and made you walk erect. (Lev 26:12-13)

But I will for their sake remember the covenant with their forefathers, whom I brought out of the land of Egypt in the sight of the nations, that I might be their God: I am the Lord." (Lev 26:45)

The nation of Israel understood the significance of having a living all powerful Being be their God; but, neglected the conditions required for that privilege (Ex 19:4-6); they disregarded or blithely conducted their covenant commitments and attributed the blessings of God as their own achievements. The nation did not have a desire to know God and seek His favor.

'You yourselves have seen what I did to the Egyptians, and how I bore you on eagles' wings and brought you to myself. Now therefore, if you will indeed obey my voice and keep my covenant, you shall be my treasured possession among all peoples, for all the earth is mine; and you shall be to me a kingdom of priests and a holy nation.' These are the words that you shall speak to the people of Israel." (Ex 19:4-6)

Say to the house of Israel, "Thus says the Lord God: Behold, I will profane my sanctuary, the pride of your power, the delight of your eyes, and the yearning of your soul, and your sons and your daughters whom you left behind shall fall by the sword." (Ezek 24:21)

In the course of making the New Covenant, God repeats His promise to Abraham to be God to his descendants. And God is not ashamed by those genuine Believers who call Him their God.

But when they came to the nations, wherever they came, they profaned my holy name, in that people said of them, 'These are the people of the Lord, and yet they had to go out of his land.' But I had concern for my holy name, which the house of Israel had profaned among the nations to which they came.
"Therefore say to the house of Israel, Thus says the Lord God: It is not for your sake, O house of Israel, that I am about to act, but for the sake of my holy name, which you have profaned among the nations to which you came. And I will vindicate the holiness of my great name, which has been profaned among the nations, and which you have profaned among them. And the nations will know that I am the Lord, declares the Lord God, when through you I vindicate my holiness before their eyes. I will take you from the nations and gather you from all the countries and bring you into your own land. I will sprinkle clean water on you, and you shall be clean from all your uncleannesses, and from all your idols I will cleanse you. And I will give you a new heart, and a new spirit I will put within you. And I will remove the heart of stone from your flesh and give you a heart of flesh. And I will put my Spirit within you, and cause you to walk in my statutes and be careful to obey my rules. You shall dwell in the land that I gave to your fathers, and you shall be my people, and I will be your God. (Ezek 36:20-28)

For this is the covenant that I will make with the house of Israel after those days, declares the Lord: I will put my laws into their minds, and write them on their hearts, and I will be their God, and they shall be my people. (Heb 8:10)

These all died in faith, not having received the things promised, but having seen them and greeted them from afar, and having acknowledged that they were strangers and exiles on the earth. For people who speak thus make it clear that they are seeking a homeland. If they had been thinking of that land from which they had gone out, they would have had opportunity to return. But as it is, they desire a better country, that is, a heavenly one. Therefore God is not ashamed to be called their God, for he has prepared for them a city. (Heb 11:13-16)

In the New Testament, Jesus highlights the significance of knowing a human being with an emphasis placed on divine presence within the Believer.

Not everyone who says to me, "Lord, Lord," will enter the kingdom of heaven, but the one who does the will of my Father who is in heaven. On that day many will say to me, "Lord, Lord, did we not prophesy in your name, and cast out demons in your name, and do many mighty works in your name?" And then will I declare to them, "I never knew you; depart from me, you workers of lawlessness." (Matt 7:21-23)

Whoever has my commandments and keeps them, he it is who loves me. And he who loves me will be loved by my Father, and I will love him and manifest myself to him." Judas (not Iscariot) said to him, "Lord, how is it that you will manifest yourself to us, and not to the world?" Jesus answered him, "If anyone loves me, he will keep my word, and my Father will love him, and we will come to him and make our home with him. (John 14:21-23)

Well after the end of human history, Revelation reveals how the image of God, God's very good Creation, is restored from sin's corruption.

And I saw the holy city, new Jerusalem, coming down out of heaven from God, prepared as a bride adorned for her husband. And I heard a loud voice from the throne saying, "Behold, the dwelling place of God is with man. He will dwell with them, and they will be his people, and God himself will be with them as their God. (Rev 21:2-3)

Then the angel showed me the river of the water of life, bright as crystal, flowing from the throne of God and of the Lamb through the middle of the street of the city; also, on either side of the river, the tree of life with its twelve kinds of fruit, yielding its fruit each month. The leaves of the tree were for the healing of the nations. (Rev 22:1-2)