Yes, you can change your Player Name and pick from an in-game Avatar option through the League.

To change your Player Name:
  1. Select the "Members" tab at the bottom of the screen
  2. Tap on yourself in the League roster (you will be the one highlighted with a purple background)
  3. Select the edit icon at the right-side of the red banner
  4. Input your desired player name or tap on the dice button for randomized suggestions
  5. Select "Confirm"
To change your Avatar:
  1. Select the "Members" tab at the bottom of the screen
  2. Tap on yourself in the League roster (you will be the one highlighted with a purple background)
  3. Tap on your current Avatar
  4. Scroll through the in-game Avatar options
  5. Once an Avatar is tapped, it will immediately be applied. If you want to make a different selection, repeat steps 3 and 4.