To change your username and avatar on Ethfinex, you must have submitted a discussion topic or comment to the forum.
If you haven't submitted a post yet, submit a discussion topic and rate your favorite Ethereum project.
If you have submitted a post, locate the topic and click on your username. Doing this will open a pop-up through which you can press edit. Pressing edit lets you personalise both your username and your user avatar, allowing you to leave your mark on the Ethfinex discussion boards.