A game's name is set by the game creator. It's displayed prominently on the My Games page for all participants and also mentioned in e-mails about that game.
Games names are limited to 50 characters.
Games that are part of a tournament are named via the tournament's name, plus a suffix to identify the position of the game within the tournament. If the tournament's name is too long to fit completely, it will chop off the end.
Games that are part of a ladder are named with the ladder's name and the participants.