I can see merit in many postings above. It can be approached from two positions, emotional and logical. Logically, the child carries the Father's last name. Now, I loosely say, this is the "traditional" method, as traditional relationships seem few and far between these days. Emotionally, you need to consider whether your child will be demeaned or harmed in carrying the Father's name. Or rather, your own negative feelings towards the situation preclude you from using the Father's name. Is it for you or for your child's benefit? In the case of a simple 'sperm donor' scenario, it may be justifiable for the child to carry your name. A clever ideas was to use the Father's last name as a middle name, and give the child your own maiden name as a last name. After all, you are validated in being proud of your own heritage and family.
As far as being called by the wrong name, as a divorced mother... get used to it. Most often, you, if not addressed by your first name, will be addressed by your child's last name. this happens routinely with coaches, teachers, physicians, etc. Don't be offended. They are linking you to your child, your pride and joy. Save the name correction for a more suitable time. Jayden