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

My daughter is 3 years old. Her father was involved in her life till she was 2 months old, so he is on the birth certificate. She was born in Kentucky and at 3 weeks old, my daughter, her father, and myself moved to Illinois. Her father and I broke up and he moved back to Kentucky. A child support order was put in place but he refuses to keep a job long enough for child support to find him and get anything. He has not seen her since August of 2005. I have no contact information for him. I have talked to his parents but they do not know where he is either.

My daughter has his last name, but I want to change it to my last name. Since I do not know her father lives how do I go about doing that? Do I still need to do a legal publication in the county I am filing in?