Congratulations to you and Sophie for now having the same last name. I kept my late husband's name so that, after he died, my daughter and I would share the same last name. Even though I'm remarried I'm still McLain.
Could you have accomplished the name change if you told the court he was dead? Or that he disappeared on you? Seems like the court was only interested in upholding the patriarchy and not in the sound, heartfelt desires of a little girl.
Shame, shame, shame on him. I know you are struggling financially. He has never supported you, except in the most rudimentary way so why give him any toehold. Sadly, unless he changes, he will never be the man he should be. So, I'm not sure filing on him for child support will give you peace. I guess it is righteous though. And logically, he should bear some of the cost of raising Sophie.
But not if that gives him entry to inflict damage. Enough of this toxic jerk!
The courts are disappointing but the sperm donor will always be an asshole!