In Illinois, child support is subject to a mandatory formula specified by Illinois law. Judges have some discretion in adjusting the amount, but evidence must be produced and accepted by the judge in deviating from the statutory formula. As you noted, for one child, the amount is 20% of net income (whether student loans are adjusted for does not seem to be technically specified by Illinois' statutes, though such expense may be a reasonable and necessary expense for the production of income). Medical insurance, taxes, mandatory retirement contributions, and some other items may be deducted.
As far as the name, I don't believe a name can be changed without the custodial parent's consent. Another attorney may wish to chime in to confirm this, however.
This answer is only intended for informational purposes and is not, and is not intended to be, legal advice for any specific individual's legal situation.