Legality of using someone else's name to start and run a business

[Dave A]

but due to him still being under a company, he says that would be a conflict of interest, so instead he wants to register the business under me, his younger brother, and take it all from there. Then, two years later, after he leaves his job, he'll switch back ownership to his name and continue with it. Is it a safe and good idea to agree to have the business under my name for the time being?

That process does not in any way mitigate the conflict of interest and the legal consequences thereof for your brother. To some extent, it makes things worse as there is now deliberate deceptive methods being used...

Look, I'm not a lawyer and I'm not even going to attempt to say anything about the legal aspects.
However, it is plainly unethical. And that's normally a pretty good sign that it's a bad idea.