Surrogacy for my adopted Mom?

My adoptive mom (not legally adopted seeing as im 23 but shes my mom to me no less) Had a hysterectomy a few years ago and her and husband want another child. We want to do it just between us, her husband making a "donation"; an at home insemination if you will. Now my question is, when I give birth I do not want to be on the birth certificate. This is my adopted parents child not mine. Is this possible to do or are there legal issues in this situation and if so whats the solution?