Then for each name, they should associate a Game of Thrones character. It should be done based on personality rather than physical aspect.
To avoid upsets, it may be a good idea if everyone writes with capital letters, making it harder to identify the author. But remember it's only a game and take it easy even if you were associated with "Reek" or "Shae".
After the game you may learn a lot about you as a person. Do you see yourself the same way as your friends do? Do they see you all in the same way or each in his own way?