Can I change my daughter's surname to mine, if so, how?

When I was five months pregnant until my daughter was eight months old her father was in prison. While there, he kept insisting his name be on her birth certificate and sent me a power of attorney so I could sign it for him. I called the vital records office who said I could not use that document to sign for him. Turns out it's not for things like that it's for financial decisions. After her birth and talking with the woman who brought in the paperwork for the birth certificate, she said if she left the room she didn't mind if someone signed in his place and against what everyone advised me not to do she was given his last name and someone in my hospital room signed his name. A few reasons I want to change her surname back is: 1. He was not even there to sign; 2. While he loves her and sees her multiple days a week, she lives with me and he would never have the money to take care of her financially nor does he pay one cent now. He is on probation with 7 felonies and used to be a heavy meth user. Thankfully he's been clean now almost 3 years and lives with his sister and her family who are great people. I got my daughter out of it! And she changed my life so much I make great money and pay for private preschool and she has no shortage of love and never has to worry about not being provided for; 3. He is still married and I just thought she was his ex. They have 2 kids. So basically my child is a bastard child and shares a last name with his wife and kids; 4. Her first and middle names are family names but I realized after the fact that her first and last name was the name of a woman murdered in the 90's by someone very famous. If I said her name you would know instantly. It's embarrassing to hear anywhere it is called out loud. So embarrassing that at her preschool I hyphenated my last name into it and yes he does know I did that and why. Sorry that was such a rant. My question is what are my chances of getting her name changed based on my reasons?