It's illegal in several ways. First "public domain" means there is no assertable copyright in the picture--but it does NOT deprive the person who's image it is of the right to control the use of their image. Second, representing yourself as someone other than who you are could be considered, depending on the exact circumstances, either identify theft (of the identify of the person whose picture it is) or fraud (upon people who respond to you based on the representation that you look like the other person). Third, it is most likely violation of the terms of service or use of the dating or networking site.