Can we change the Theme info like Theme name and author link etc


I am not sure whether I am asking the right question or not. I am planning to start a membership website for one of my clients who wants a wordpress like site on which users can pay for their sites and get access to premium plugins and themes. I just want to know, whether is it legal to modify the footer links and theme info like author link and theme name etc ? the only reason is that the client does not want the customers to leave their website and wants his links on the themes etc.

And if it is legal to do that, would he still be able to get the theme updates using wpmudev ?

Please advise