Names are important. When we meet other people during the day, we often address them by name. With people we are meeting for the first time, the first thing we do is ask their name. Knowing someone's name makes us more comfortable. It feels like a starting point. It gives us a sense of familiarity, like we know and therefore can trust a person if we have their name. They are more accessible to us in a way.
Sometimes, with meeting a new person, we are reluctant to give them our names. We may not trust what they can do with that information. Will we be judged or labeled for the name we have? By our family name? In a town where our family name means something? either from a good history or a bad one? Sometimes we acquire nicknames with our friends that define how they see us. Sometimes nicknames aren't very nice.
Genesis, the first book in the bible, is full of names. It is full of sons and daughters, and which begot which and even what "tribe" or "type" of people later descend from them. Some of these names change over time. Abram becomes Abraham and Sarai becomes Sarah. Jacob becomes Israel. This often happens at a turning point in that person's life, when they give their lives over to following God, like with Simon, who becomes Peter.
Nowhere in Genesis can we find God's name. He is simply called "LORD" or Adonai. He is often addressed as "the God of Abraham, Isaac, and Jacob." And these are all true. But it isn't until hundreds of years and many lifetimes later, in Exodus, in slavery in Egypt, that God tells Moses his name.
We see Moses ask, at the burning bush, "who shall I tell them sent me." He has to press God about this and the answer he gets is unexpected. It almost seems purposefully vague, a non-answer. He says "tell them I am sent you." "I AM"? Sometimes this is translated as "I am who I am" or "I am who am".
Could you just imagine picking up the phone to answer it and the stranger on the other end only identifies themselves as "well, It's me, you know, I am who I am." That's what God's answer in scripture sounds like to our ears at first. But it is so much more.
Scholars have thought this over for hundreds of years since then. God gives us His name and it identifies Him as "being". God is "being itself". He is realized as the only being in existence that can claim this. The only one who is outside of everything, who made everything and called it into existence, who's existence is eternal, without beginning or end, who was not created and whose existence depends on nothing else outside himself. He is the only one who simply IS. In a way, we can never say "oh He was" or "He will be" but it is always "He is." God is a constant, and I find that comforting.
It also makes sense, in a way, for the All-Knowing One to "be". He doesn't have to remember the past or predict the future. It is always the present to him, and he is present to all of us, no matter the time or place.