Under most circumstances, your name will not be shared with anyone, and your name will NEVER be shared with the Caretaker or Fleet Commander you are leaving a survey for.
With that said, there are some instances where surveys will be shared with members of Horde Leadership for further investigation. If Horde Leadership requests your name so they may follow up with you personally, your name will be shared with them.
Let it be known that
Atomic Pancake,
Fim Asatru, and
Rossonius Pun have access to the surveys. As a result, they have unrestricted access to your name.
If you have questions or concerns about the Caretaker program, you may reach out to any of the individuals above.