This question is a bit more complicated than a name change. It really has to do with determining and possibly terminating parental rights of your daughter's Father. If as you say he left denying paternity then he may not care if you do terminate his rights to her, but that also terminates your rights to support (should you seek it somewhere down the road) and her rights to inheritance from him and his estate (also some day down the road). Do not worry so much about not knowing where to find him. The law has provisions for service on those we do not have exact addresses for. It just takes a bit more effort and more money and time. You may want to instead consider changing your daughter's name to add yours as a hyphenated name in the meantime. This will help with issues such as making decisions in school and even health insurance claims. You may also want to seek help having you officially declared the custodial parent by the courts. Good luck.