You may block a player from starting future games with you or chatting to you.  Tap their chum in the game screen and swipe up on the "Stats" screen to see the "Block" button.  You can also block them by tapping their name in your leader board on the main screen.  Swipe up on the stats screen to see the block button. 

A blocked player will not receive a notice and you will not receive any chats from them and they will not be able to start a game with you via username.