Legal Question in Family Law in Illinois

Grandparents have visitation rights.

It makes no difference whose last name the child has. It is entirely irrelevant to what visitation rights the grandparents may or may not have. If parentage has not been established, i.e, by the signing of a voluntary acknowledgement of parentage or by a court of law, the father has no visitation rights other than what you may choose to give him. The GP's have none at all. As a rule, GP's have access to the child through the parent to whom they are related. If that parent is living, they see the child when he does. Other than that, they have no particular rights regardless of what some may believe and you have every right to deny them access to your child if you don't believe that it is in his interests to spend time with them. OTOH, you would be well advised to "play nice" since grandparents can be an enormous help to you when their own son refuses to help you with the child out of spite or other reason. My advice is to "play nice" whether you have to or not.