I need to know how to add the fathers name to birth certificate years after child is born and changing child's last name.

Whose father? Yours, your child's? Would you want to change the child's last name?

You need to get an Application for a New Birth Certificate Based on Parentage form from the vital statistics in the state and county the baby was born in.
If you gave the baby some other persons last name I think you have to get their permission.
Like if you gave the baby a boyfriends last name
If you gave it your last name it shouldn't be a problem.

It does cost to change it.

Whose father? Yours, your child's? Would you want to change the child's last name?
Yes I want to put child's fathers name on her birth certificate she is now 14 we r now married and yes it would change her last name.