changing an almost 2 Year olds last name

My daughter's father hasn't been around since she was 5 months old. Well in June he randomly showed up and was seeing her regularly for him then after 2 weeks went to only seeing her on sundays which lasted 2 weeks to him not showing up, not calling nothing. So He hasn't seen her since the very end of June and I haven't heard from him. He refuses to give me an address of where he's staying, he claims he's homeless but he's living with his girlfriend an hour and a half away from us according to his grandmother, I don't have a phone number for him and I had to block him on Facebook due to him posting my pictures of our daughter talking about how horrible of a mother I am and writing me talking about my unborn son who's not his. Any advice on how to even file that in court since I don't have an address to have him served. Also I have full custody of her and he's $2,000 behind in child support which I didn't even know if they'll look at that.