Multiple domain names for one site

What you’re trying to do is called Domain Masking. There are several ways to achieve this, but they are not easy.

There is a plugin in the repo that seems to be able to do content masking right from within the dashboard, but I have never tested it.

My initial intuition would be to do it using htaccess and apache’s mod_rewrite module. You can see an example here, and there are plenty of similar questions/answers on stackechange which you can google.