When you know someone’s name, you can speak it and the name’s owner instinctively responds. It even happens in our sleep that when someone calls our name, we wake up. To know someone’s name is to have some “control” over him or her. So, to possess God’s name would mean we have some control over him. But that cannot be the case because God is almighty and we can’t have any sort of control over him. It would be a contradiction of term “almighty” if we did.
Sure we can call on God whenever we want, and he does want us to call on him as a child would a parent. But because we don’t have his “name” we remember he isn’t someone at our beck-and-call. The lack of a name reminds us that we have to be respectful.
You might say God has a name and it is “Jesus.” Yes and no. Indeed, Jesus is the name of God-made-man. But Jesus means “God saves,” or more literally, “I AM saves.” So, although it is a “name” in a sense that he was given a name during Christ’s circumcision, it also is a lack of a name in another sense because it just completes what God answered Moses in Mt. Sinai – which is his nature.