The winner of any game of Jean-Luc Picard is the person who says "Jean-Luc Picard" last. A telephone game is quite easy, as you can just hang up after shouting it - in real life, you can't really run off because the other person will just shout "Jean Luc Picard", and it's difficult to keep shouting at each other as you walk away, and work out who heard who say "Jean Luc Picard" last.
The answer is to calmly intone "Jean-Luc Picard", then put your hands over your ears, and run away squealing. This is both dignified and mature.