My question involves name change laws in the State of: ILLINOIS

I have a 2 year old daughter and am pregnant. My baby is due here soon, and I need to make a decision on his last name. My 2 year old has her father's last name. He has made zero attempt to help take care of her, I receive no child support and he has not even been employed the entire time she has been alive. I also have a 4 year old daughter who is not by this man who has my last name. I do not want to give my newborn baby their father's last name (the same as my two year old). I would like to give him mine and have my 2 year olds changed to mine as well. Although I do not even know where their father lives now, I know that just out of spite he would not just openly agree to this. Is it possible to have my 2 year olds last name changed to mine and if so how do I do it?