I don't know... I could go either way. I can see pros and cons for both, and don't think its a clear, cut and dry choice.
Doctors don't generally test for paternity when filling out the birth certificate. They put what they've been told. And they can obviously be told wrong.
Ultimately, its your name and your decision. An explanation (as you've done already), is probably best, for future generational historians, since the record says one thing. You could, in fact, have your birth certificate legally altered to reflect the now known truth, if you wanted.