Minor name change

I want to change my daughter’s last name and I’m wondering if anyone else has gone through a similar experience, can share advice, thoughts, etc. I have the paperwork and all I have to do at this point is fill it out and mail it in to begin the process. My daughter is 5 years old, she hasn’t seen her biological father since she was 1 and she has no idea that my husband isn’t her real daddy. My husband has been in her life since before her 2nd birthday and has taken her in as his own. We have another daughter together who is a little over a year now, we own a home, have pets, and we’re basically just your ordinary, happy family. We want all of us to share the same last name as a family. My 5 year old’s biological father has never made any attempts to see her other than posting on Facebook to try and make me look like the bad guy, asking if anyone knows my whereabouts- I know this because we share a couple of mutual FB friends that messaged me to warn me that he was looking for my address. I have him blocked on social media because I don’t care to see him or hear from him; the last time I saw him, which was the reason for our split, he attacked me in a drug-fueled rage (I won’t go into detail) and I filed a police report. He was arrested and pleaded guilty for assault and the judge filed a danco so he was not allowed to contact me; however, his family could contact me in regards to my daughter. His grandma contacted twice, once to say that I HAD to allow my ex to take my daughter (which was a lie) and another time to ask if she could see her. I allowed her to visit with my daughter, but after that visit was over she never contacted again. It wasn’t a loss in my eyes. So anyways, it’s been a few years, my ex hasn’t made any real attempts, I don’t know where he lives or much about him at this point. I can’t imagine he’s made any major changes. The way I see it is if he wanted to see her bad enough then he would file the right paperwork through the county that he lives in and go from there, but he would have to pay child support and I think that’s one reason that he hasn’t made any attempts. The one thing that has always kind of held me back from filing the paperwork for the name change is that he’s on the birth certificate, so I may have to publish something in the newspaper and he could show up to the court hearing and the thought of seeing him after what he did to me makes my heart beat so fast, just thinking of it now gives me terrible anxiety. I still have nightmares about him, and it’s been over 4 years. If I saw him or had to speak to him I don’t know how I would react, and my daughter would be SO confused because she thinks my husband is her real dad. I have no idea how I would have that talk with her, and my husband gets sad about it as well because he knows eventually it’s a discussion we’ll have to have with her. It’s all just so confusing and sad and makes me so anxious. Sorry for the long post and if you’ve read this far then I thank you and if anyone could offer advice or their thoughts and experiences I would so appreciate it. All I want to do is the right thing for my daughter and for our family. I’ve asked her if she would like all of us to share the same last name and she says yes, I’ve told her we would have to see a judge and it’s not as easy as it sounds and she just smiles and says okay. I just want what’s best for her and our family.