As an egg donor, you will likely be asked to reveal a lot of personal information - both medical and otherwise. At the same time, though, you do have the right to privacy. It is up to you to decide how much information you are willing to reveal and how your information will be used.
Questions to ask:
Who has access to my medical information?
Make sure you are aware, before being tested, who has and will have access to your medical records; whether any of the results need to be submitted to the state; and how the results could affect your medical coverage.
How is my confidentiality being protected?
Most programs use numbers or codes, instead of your legal name, on any paperwork you turn in or any medical records they keep. However, this can differ from program to program. It is your responsibility to figure out how your program views and maintains confidentiality.