Just keep clicking the green flag until you receive a litter you like! Sometimes (Rarely) Two kits will have the same name. There's not much I can do about that. If you like the name but not the colour, you can go into the coding and change the costume. Thats what I do :) There's a one in ten chance you'll get a litter with one dead kit.
Inspired by @FunWarriorcats Feel free to comment your litters! I had one kit in my litter, a she-kit called Birdkit