When I marry my girlfriend can we change her daughters last name?

Changing her last name is a process. First off, yes you need the fathers permission whether the father is on the birth certificate or not, cause changing her last name to yours ultimately means you adopt the child as your own, and this could disrupt any child support you may be receiving from the father if you are currently receiving anything. This happened in my case where my ex left me for another man while I was deployed over seas in the Marine corps, my son was born when I was away , and didn't put me on the birth certificate but put my son to have my last name. I come back and she demands child support, but denies me visitation, she got married and kept my sons name as is cause changing his last name would require me to sign off and give up my rights as his father . To this day he still has my last name, I still pay my monthly dues, and still don't get to see him.