You should talk with support or your licensing manager.
You can get multiple domains assigned to your license and for it to work. The rule is that the sites pages are essentially the same page. sitea.com/home and siteb.com/home is the same page.
If you want to run a different site you can have one license with two domains which serve different running instances. (You can buy a second domain for a cheaper price and add it to your license)
If you are looking for more of a one instance multi site running - there is of course the multi site license but you can also look to use URL rewrite to direct sitea.com/home to the internal page /sitea/home and siteb.com/home to the internal page /siteb/home (But you mentioned you don't like that idea)
But first, talk to Sitefinity license manager - explain what you want to do and they can ensure you do it the right way for your situation.