That depends on how players will get matched and ultimately connect to your server. If you use our lobby-based matchmaking facilities, the sequence will go roughly like this:
Players make a FIND_OR_CREATE_LOBBY call to the LobbyService. The lobby matchmaking process runs and a bunch of players get associated with a lobby instance. Once the launch conditions are satisfied, brainCloud will launch an instance of your dedicated server. The dedicated server will start and immediately make an S2S call to ask brainCloud for all the lobby instance details. These details will include each players name.If you don't use lobby matchmaking, you'll need to use the S2S api to query brainCloud for the player details manually.