Your Product Hunt profile image is tied to either your Facebook or Twitter profile image.
To resync your profile image, or change where it is being pulled from, you can go here and select the option to sync your avatar with Twitter or Facebook.
It will take a few minutes to update everywhere on Product Hunt. You may need to clear your browser cache to see the new version right away. On a Mac, you can do that with the shortcut CMD+SHIFT+R.