You should absolutely tell your doctor about your medical ID. This is very important to confirm accuracy and so they are aware you have an ID on you. You may want to show them your ID on your next doctors appointment to get their approval of information and visibility of engraving.
Also when you print a medical ID wallet card online you will want to be sure that information is correct as-well. If needed you can always ask your doctor to visit our website (www.My-Identity-Doctor.com) to print you a wallet card and fill it out accordingly.