Firstly, If an adoption order was granted your daugther father would cease to be her legal parent. This would end to any rights her father may have to custody, guardianship or access to her ect. If he is seeing her every second weekend I don't think he would sign away his rights, even if he did, it wouldn't be easy to get though court. I don't think it would be fair to take your daugther's father away from her either. She can still have a relationship with your DF but I think its important for her to have her father as well.
You should be able to change her name but I think you will need her father's permission, you just apply to Births, Deaths and Marriages.
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