The main reason you wouldn’t use the full name on a picture is privacy concerns. Some teams don’t list last names on their website (even though it’s terribly easy to find someone’s last name on the Internet, mostly a courtesy measure).
Other things to consider include how you would read the picture when showing it to someone. “Oh, there’s Chris yelling at the drive team”. It could potentially be strange to use the full name, unless the picture’s purpose is to introduce someone.