My son was born in Illinois in 2010. When he was born his father signed the birth certificate, so I hyphenated his last name to include his father. We have never married and he has never paid child support for my child. I am in the process now of going after him for the support. What do I need to do to get the hyphenated name off my child's name?

His permission. Would need that even if he was not listed on the birth certificate ( but with it on, at least it is easier you don't have to prove he is the father.

A birth certificate is a legal document. To amend a certificate, except to correct minors factual errors, requires a court order. The father would have to agree in court to the change.

If you are only first going after him for support then he was never legally required to pay support. So the fact that he hasn't will have no bearing.