Does God have a name?

When God told Moses to go to Pharaoh to demand that the Hebrews be set free, Moses asked God, “Suppose I go to the Israelites and say to them, ‘The God of your fathers has sent me to you,’ and they ask me, ‘What is his name?’ Then what shall I tell them?” (Exodus 3:13) Was Moses being presumptuous? And what does God’s answer mean?

I don't think that Moses was being presumptuous. I reckon he was just trying to anticipate the kind of questions the Israelites might ask him and as for the meaning of God's answer, well it simply meant He is who He is and who is He? He is the Living God so simply put God told Moses to tell the Israelites that the Living God has sent him.