Why did God tell Moses, "My name is 'I am'"?
The story you refer to, from the book of Exodus, offers us much to explore. Moses sees a burning bush. As he draws near, Moses is invited to take off his shoes because he is in the presence of God. When Moses asks for God's name to bring back to the people, God gives this name: "I am." Note that the verb God uses is present tense. God is always present to us. God did not say "My name is 'I was' or 'I will be.'" No, God said his name is "I am." It is always in the present moment that God is to be found. Unfortunately, it is easy to miss God because we are often not in the present moment! Perhaps we focus our energies on the past: regretting what did not happen, being angry about how we were treated, being ashamed of our failures. But God is not in the past. Or maybe we focus too much on the future: looking forward to some event with excitement or anxiously worried about what we face. But God is not in the future. Where is God to be found? Always in the present moment. "I am" is the name of God. It is only as we become aware of being alive in this very moment, wherever we are, that we will be able to become aware of God. Whenever we remember God, God is already there, present to us!