My question involves name change laws in the State of: Florida

My 4 year old daughter has my maiden name and I would like to change her last name to my married name. The father is not on the birth certificate, but he used to pay child support and as such has been found to be the father through paternity tests. He has since stopped paying and moved to South Carolina. I have been married for about two years and have another daughter with my husband, but I would like my girls to have the same last name, we tried to adopt, but my ex ( although he said he was okay to sign away his rights as a father and has showed no interest in being a father, she has never met him ) always made excuses and missed appointments to meet with notary. I have no address and the only contact that has ever worked has been through Facebook... I just wanted to give as many details as I could as the majority of the threads do not pertain to my situation.