So you mean here that you would need to rewrite the urls to reflect the new domain?
Well, in my opinion, you should always publish Linked Data under a domain that you control. You are responsible that it stays dereferencable, that people can work with it. However, I have to add: if your WebId allows to dynamically find all the rest of your data, then you “only” need to make sure that WebID url remains the same. And the moment you move, you make sure that the urls in the your profile are updated.