DO NOT use the RENAME button in the game lobby screen.
It will NOT change your in-game name. Do this instead:

1) Close the game.
2) Open the launcher if it's not already open.
3) On the left menu bar, click PARAMETERS.
4) Make sure the box beside Profile Name is checked.
5) Type the name you want in text box beside Profile Name.
6) Click on the SERVERS tab on the left and join the server.