My understanding is that if you're registering at the post office, you'll need to go there with the person who owns the place you're staying at. If your ex can't go or doesn't have her passport, I suppose you could just take along any Russian with a passport who will claim you are staying with them. As far as if you can just show up at the post office by yourself and try to register, I don't know. I've never tried it because I don't speak Russian. If you do, you can always try it by yourself and they'll tell you if you need the owner to register.