Quote Quoting hgffrank
Can I get my daughters last name changed to my last name even if the mother objects to the change.
You would have to either obtain the mother's consent, or obtain a court order requiring the name change by demonstrating to the court that it is in the child's best interest to share your surname. That would be a high burden to meet.

Quote Quoting hgffrank
And what do I have to do to have my name listed on the birth certificate as the father.
You can download the form to correct a birth certificate here.