Let the other person know that you would prefer to be known by the handle you use or even better, you could tell the person to call you a pet name but let the person know that it is indeed a pet name, because at a later date, if the relationship really blossoms it doesnt look nice if you have to say something like, “Gee, I’m sorry, but my name isn’t really Janice, it is Heptullah, I guess I lied to you.”
The best thing in this case would be to let your self be known by the name of some celebrity. You could call yourself Cinderella or Pocahontas or Archie, or Betty or Veronica. The chatting has now begun and you can start exchanging information. Keep to the general and stay away from the specific.