Because that is what Ex 3:15 says. He may have many titles but only one name. Same as others.
Moses was right, because Moses says so? It's circular reasoning. But, it's our tradition, so let's just stick with the story just as he gave it.
Can we agree that it's Moses' account that we have, and that we call the books of Moses? And if it was to some degree, a chronological telling-- like a story that started in the beginning with creation, on through the flood, to Abraham, Issac and then Jacob-- and then Jacob's the story of Jacob's 12 sons-- and of one of those son's Joseph who ends up in Egypt--- and then 500 years is skipped and we get to this narrator of that whole story I just summarized-- this Moses, who like the prelude to an epic movie, has been narrating the story thus far, and now in Exodus we get to the main character and his life story....
The name of his God is well established.... it's the name everyone else is going to use going forward... all the prophets and poets, priests and puppeteers-- why? Because that's the name we were given. Everybody uses Moses as the answer key. And Moses said it was Yahweh.
There was this angel I encountered. The angel of Bob. Bob did this and Bob did that. It's always been Bob. Only Bob. And Bob's angel was sent to me and I'm here to tell you that Bob is above all other names... Almighty Bob. In fact, whenever we think of a Supreme Being, I want everyone to call him Bob-- got it?
And everyone did.
Wups. Except Jesus. Jesus said call him Daddy.