U-235 was never U25, it was just 25. Or 29 for plutonium. Just as a little correction.

The answer was that the code-words were meant to obscure what they were doing if you had no idea, but be very plain and straightforward for people working in the project. It is easy, in retrospect, to see how flimsy the scheme was. But it wasn't about preventing spies from finding out about the work so much as it was about preventing accidental leaks. Similarly, if you saw Nicholas Baker you probably could recognize him, but if you ran across a list of people on a train, "Baker, Nicholas" was a boring-enough name.

Early on in the work, they had tried to use other kinds of obfuscating code-names, like calling uranium "copper." This is arguably a much better code-name because it wouldn't even be obvious you were using a code-name! But what if you need actual copper? Then you call it "honest-to-god copper" and the facade falls apart pretty quickly.

Ultimately, the fact that most of their security was trained towards leaks (and not spies) makes this make a lot more sense. As is the fact that they were, in essence, coming up with this system from scratch; the people who implemented these code-words were not using some kind of standardized counter-intelligence protocols, as would happen later. Even into the early 1950s they were still using what would be, by modern standards, bad code-words (e.g., device names that described their appearance or operation, or mnemonics — modern OPSEC would be to use truly meaningless code names), until finally someone got on them to have a better system.

The Soviets, as an aside, from the very beginning used pretty good code-names on their own project. The papers of the Soviet nuclear program are very hard to wade through if you don't know what each project and substance number is (and they just assigned things numbers). It's all Project 602, Substance 143, Site 2, etc. Very hard to parse. The Soviet approach to secrecy was much more deeply ingrained than that of the Americans, who came to it relatively late and were essentially just making it up as they went along in the early days (the code-name system in the early US nuclear program was developed by a handful of scientists, not security professionals).

For more details on why thinking about Manhattan Project security as counter-intelligence, as opposed to counter-leaking, is not quite right, see the chapter on the Manhattan Project in my book! :-)