If a convert (orthodox) later finds out she was Jewish anyway through her mother, does she need a new ketubah since the one she has says bas Avraham and giyorta? Would the answer be different if the biological father was Jewish or not Jewish?
A kesubah is a shtar -- a binding legal document under Jewish law -- and must meet the criteria required of all shtars. If a kesubah is found to have a mistake, it can be corrected with a kesubah dimishtakich bei ta’usa, a kesubah in which a mistake was found, that is used in these circumstances and signed by witnesses. See http://e.yeshiva.org.il/midrash/shiur.asp?id=11715. It seems to me that since both your name and halachic status (converted women are entitled to less money than born-Jewish women in the writing of a kesubah), it would seem to me that the mistake is serious enough to take to your local rabbi for further consultation.