I live in Illinois and I want to know if it is possible to change my child's last name to my own? The father abandoned us when she was just one month old and we have no idea where he is.

You can legally use any name you want as long as its not intended to defraud. For example, you can tell his school he goes by John Maidenname and they will accept it, even if the birth certificate is different.

But if you want to ochange it legally, then you will need to go to Family court and petititon them. They will have you make a reasonable attempt to contact the father for permission. If you can't, they will most likely grant the petition.