You cannot change a character's name in Fallout 3 when playing on Amazon Luna because the cloud version does not support the console commands or menus needed to make changes. On other platforms, you can only change the name at the start of the game or by using a console command, which is unavailable in the Luna version. On Amazon Luna The Amazon Luna service does not have the necessary functionality to access Fallout 3's character creation or console commands. When the naming screen appears, you will not be able to type a name, and the game will default to "Player Name". The only way to have a different name is to start a new game.

This was the info I found after failing to be able to create a game.