We have made sure that the share feature in Coding Jam is completely safe. It's externally reviewed and vetted by the KidSAFE program:
No personal information from your child’s account is ever shared (including your profile name). Along with the jam itself, the only thing that is shared is the randomly generated 3-word "band name". This cannot be tied to your account by the people who will see the song.
There is currently no option to disable the share feature.