You will have to give Dad notice and attempt to get permission. If he doesn't contest, you should be able to get the name change completed. Getting permission will make the process move smoothly and avoid delay.
Whether he consents or not, you have to file a Petition with the Court, publish the Notice, and mail a copy of the Petition and Notice to the dad. If he objects, he would need to file an Objection. You would then argue why it is int the child's best interest to change her name. And it appears she is not asking to get rid of dad's name, just add yours. This should be a relatively simple argument since you are her sole custodian.
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