I'm not sure you can change it. I know when you challenge someone to a game, that is where you can set the name.
Resolved: Naming a Game

Yes you can name the game. Wait one minute and I will edit this with instructions
- click "Play"
- Click "online ches"
- Click "Start new game" in the box on the right of the screen
- Select "game options I choose"
- about 4 or 5 boxes down you will see an optional box to input a game name
Hope that helps
I'm new to chess.com and I can't find instructions on how to change the name of a game from "Let's Play!" to something else.