Because of the complexity of the atomic bomb, and because of the rushed way in which it was created, there is simply no way that one person can be identified as the inventor of the bomb.
However, there are a few people who are most connected to the bomb in the public mind. The first would be Albert Einstein since he signed a letter to President Roosevelt urging an all-out effort to create a bomb. But it was not his idea and he was asked to draft the letter since he had a big name and would get attention. The second is J. Robert Oppenheimer. He was in charge of the laboratory at Los Alamos, New Mexico, where the bomb was created. But that does not mean that he invented the bomb, just that he was in charge of all the people who worked together to make it. The last name is General Leslie Groves. He was in charge of the entire Manhattan Project which created the bomb. Like Oppenheimer, he did not invent the bomb. He was just in charge of the entire project (including all the parts of the process that had to happen to allow Los Alamos to build the bomb).
There is no one inventor of the atomic bomb. These three have their names connected to the bomb in the United States, but there were thousands of other scientists whose work was critical to coming up with the idea of the bomb and making it happen.