Your Avatar is based on the Hero that is currently selected as your Major. Your Major is the hero that represents you in the Warzone, and their picture will appear on your profile, in chat, and anywhere Portraits/Avatars are visible. You can change your Avatar by changing which Hero is your Major.
To change your Major:
1. Tap the Hero avatar in the top-left corner to navigate to your Profile
2. Select 'Major' on the bottom navigation bar
3. Choose the Hero you'd like to appear as your Avatar
4. Tap Confirm to save your changes
Keep in mind that your Major is the primary Hero whose stats and benefits apply when sending attack marches or defending your base. You can unlock more Heroes and their Avatars from Event Prizes or Sales.