There's a thread here somewhere with this game. I can't remember the name of it, so I can't find it. Credits to whoever first created it.
Player one posts a scenario: family is expecting a (boy/girl). She wants the name __________. He wants the name _________.
Player two posts a compromise name for player one's family. (Usually somehow combining the two names or finding a similar sounding name). Then player two posts their own family scenario.
So, it may look like this:
Player 1: "Jack and Elizabeth Abbott are expecting a son. Jack wants to name him Nicholas James. Elizabeth wants to name him Maximilian Jase."
Player 2: "Jack and Elizabeth chose Nixon Jay."
"Stephen and Amy Phillips are expecting..."
Hope this make sense. I will post the first scenario in the comments.