How to change my daughters surname

I gave birth with my first daughter last November 2011. I and my ex live in partner were okay during that time. I registered the name of my daughter under his name (my EX). I got pregnant with my second daughter last 2012 and my ex live in partner denied the baby I was carrying. We had misunderstandings that lead to our separations. When I gave birth with my second baby, I registered the name under my family's name. I just wanted to know if it is possible for me to change my eldest daughter to my family's name. I and my ex live in partner were NOT MARRIED at all. My eldest is now 1 year and 8 months old. My daughters were under of my custody and I haven't receive any support for my ex's marital obligations with my kids. What are the process for this matter? I wanted to change my daughters name ASAP or before sending her to school soonest. HELP THERE PLEASE.