Changing the child's name will mean notifying dad and dad will get an opportunity to challenge the change. And, changing the child's last name will do NOTHING to make you a "complete" family. The child would STILL be a legal stranger to your fiance, until and unless the marriage occurs AND he adopts the child, which dad will also be able to contest. Children are resilient, they can learn new last names. It's only an issue to them if you make it one. But the courts aren't going to allow what you're describing, as it is what's known as a "backdoor" adoption, and is fraudulent. Whether dad is active in the child's life now won't impact the fact that the child has 1/2 of his DNA from dad, and that means dad has rights regarding the name of the child, and can exercise them if he chooses to.
Sorry, there isn't a simple process. The court isn't going to let a child take on a step-parent's name without an adoption. And an adoption won't even be an option until you've been married for a bit.

