Changing my babies name

How do I go about getting my babies last name legally changed to mine? I gave her her father's last name when she was born because I felt obligated but want to change it now because we aren't together and I'm doing all of the work for my baby, he only sees her every 2 weeks. (He also left us a couple of weeks ago. We were engaged and he knew how important it was to me to have my babies have the same last name as me) she doesn't have a passport or anything, just birth certificate and social security card. Also, how should I go about telling them? I have no contact with my daughters dad but contact with his mom who he lives with