Child name change

What is the name of your state? GA

I've been divorced since my daughter was a year old. She is not 8 years old. My ex-wife has re-married and has moved to CT.
I have found out that she registered my daughter in school using her new married name. When I found out, I called the school and asked them to help me with this, and to use my daughter's real last name. They said they would.
Today I recieved an email from my ex-wife saying that her and her husband want to change my daughter's last name. They want to add their last name to the end of it. They said they'd add a hyphen and then their last name.
Obviously I don't want to do this. What are my options and/or rights?

Thanks,
Bob