How can I change my baby's last name to mine?

I'm a single mother and when my baby was born I gave him my boyfriend's last name, whom I was going to marry, luckyly that didn't happen, he was abusing me. Now my baby is 2 years, I left my boyfriend and want to change my baby's last name to mine. How do I change my baby's name through the court? Do I need to present some strong reasons for the judge to change my baby's name? By my baby's birth certificate, my son doesn't have father.