How I can change my daughters last name?

I have a 3yr old daughter who's dad only was in her life the first year of her life and has been out of her life for about 1 1/2 yrs now and has no intentions of having a relationship with her he changed his number n deleted her FB account and i just found out he's having another baby with someone else. The most important reason I would like to change my daughters last name is because she gets really upset when I mention her full name when we go to the dr or at school she just doesn't like it she says that her last name is not that n mentions my last name instead so I'm not sure why she's reacting that way because I have never talked to her about her dad in a bad way plus I don't know if she even understands that's her dad's last name I've never even told her that but I have a nine yr old son that has my last name n well maybe she's confused n thinks that because he has my last name she should too it's so confusing for her so I know that it's best if she has my last name