There is some question of privacy: it might be objectionable there. But that does not really bear upon the core of copyright, which is about items that have been made public.
One could pose a similar question: what if someone else decides to dress exactly like you, and go about like that? What grounds are there for your objection to that? (There do not seem to be any . . .) If they went so far as to impersonate you in the sense of identity fraud, there is a problem. But that is really about lying rather than copying per se, like counterfeiting.