Changing the game name or database name??

Yes, you can change the name of a world. To do that, go to your game directory (Steam: rightclick on RW in Steam -> Properties -> Local files -> Browse local files) into the "Worlds" folder and change the name of the particular world subfolder. Then go into this folder and change the name of the .db file accordingly. For example, if your world is called "New World" and you want to change its name to "MyWorld", change the name of the world folder (in the Worlds directory) from "New World" to "MyWorld", and change the name of the "New World.db" file (inside this folder) to "MyWorld.db"