Engaged to air force guy, question.?

Okay so I need to know what to do to change my daughter's last name after me and my fiance become married. She's 4 months old. Somebody told me that in the state of South Carolina, its a lot easier to do before they're a year old. Unsure of how reliable that information is but I thought I'd throw it in there too. Also how soon could she get on the insurance after? Her current healthcare provider doesn't take her insurance plan provided through Medicaid/Healthy Connections. Any answers/help is definitely appreciated. Thank you ahead of time.