No. We cannot delete your name by itself, only in connection with your contact information (address, phone number, etc.). The fact that you were born with a certain name is on your birth certificate, your driver’s license, and more. It is part of the public record, and we cannot delete it.
When someone orders a DeleteMe subscription, we delete his/her contact information from this list of people search databases, not from the entire Internet at large. Under our current system of law, certain information is public and cannot be made un-public. We do as much as we can within the bounds of the law.