Am I wrong?

Sooo I ended up pregnant and after I found out the “father” told me he “couldn’t be a father to her”. He denied her and wasn’t there throughout my pregnancy and subsequently his name was not added to the birth certificate so she has my last name. After 3 years, a child support order was put into place and his name was added to the birth certificate after signing an acknowledgment of paternity however, her last name stayed the same. My daughter is now 5 going on 6. Her grandmother (his mom) was under the impression my daughter had his last name and was emotionally distraught and disappointed to find out she didn’t have his last name. My thing is, why should my daughter have his last name when he has done absolutely NOTHING for her besides providing sperm? Should I feel guilty and change her last name? Her grandmother made the statement “how can I say she’s my grandchild when she doesn’t have his last name?” Is his name being on the birth certificate not enough?