to get the exact instructions.
It will cost you $150-$200, and take about 3 months. Basically, you need to fill a form with your court and publish the name change anouncement in a local newspaper. After receiving the form your court will assign a date; on that date you and your kid appear on the court and a judge will approve the name change.
Different states may have slightly different procedure. Therefore you need to call your County Court to get exact instructions.