There is no one inventor of the Computer. Several great minds from different countries all helped invent the Computer. It might give one a feeling of nationalism or relatedness to believe a hero of your nation invented the computer. That did not happen.
Here is a partial list of the inventors of the computer and computer science: Gottfried Wilhelm Leibniz, Blaise Pascal, George Boole, Charles Babbage, Ada Lovelace, John Atanasoff, Konrad Zuze, John von Neumann and Turing.
Leibniz believed you could calculate ideas like you do numbers. Pascal built an early calculator. George Boole dreamed up a way to calculate ideas using discrete Boolean logic. Charles Babbage built a difference calculator and tried to build something even more sophisticated. Ada Lovelace is considered the first computer programmer. John Atanasoff and Konrad Zuze built machines independently which approached how our modern computers work. John Von Neumann, an international scientist, came up with the Von Neumann architecture which is the architecture that many modern computers use.
Turing just one of the inventors of the science of computers must be credited with great ideas such as the Turing Machine, a thought experiment machine which helps us study universal computation and the science of what can be computed. Additionally he did work in AI (Turing test) and with complexity. Concerning the enigma codes, rather than Turing, we must credit the Polish scientists Jerzy Rozycki, Henryk Zygalski, and Marian Rejewski for cracking the earlier enigma code with electro-mechanical machines (bombe) which Turing along with other British Scientists later refined to break more sophisticated enigma codes.
Many other "inventors" of the computer are not as well known. One I admire is Claud Shannon. Claud Shannon took Boolean's logic and mathematically proved it was applicable to electronic switches in a famous thesis. He applied it to electronic relays and was able to create a robotic rat using those switches (relays) which enabled the rat to run a maze.
Another inventor of computer science is the little known Alonzo Church who created Lambda Calculus (Lisp is based on this) which was Turing complete and proved Hibert's Entscheidungsproblem was undecideable before Church's famous student Turing created the Turing machine with it's halting problem. The Turing machine was created post (after!) Lambda Calculus only to prove the same thing. However, the Turing machine was highly credited and adopted because it is more intuitive and machine like and being a state machine is better able to handle computational theory and is useful in a myriad of ways to computer scientists.
Yet no "one" person invented the computer or originated computer science. Crediting the invention of the computer should not depend on Hollywood or Pop history rather international Human curiosity and it's prodigies, including both famous and less well known scientists, invented the computer.