How do I change my backgammon board theme?

Go to the "More" menu and select "Boards." Similar to Avatars, you'll see different board themes categorized by rarity ("Common," "Rare," "Epic," "Legendary"). Each board will show its unlock requirements, which could be reaching a certain WXP level and/or spending Galaxy Coins (GC). Examples include "Neptune," "Earth," "Helix," "Horizon," etc. Click on a board to unlock and use it.