Changing a Child's Name: Can a Father Who Has Primary Physical Custody Change His Child's Last Name

My question involves name change laws in the State of: Virginia.

I never married my child's mother, and I was unable to see my daughter until she was 9 months old. Went through the court system and proved that I was the biological father of my daughter. Went the long way through the system, and eventually was granted Primary Physical custody. Had to jump through hoops to get my name on the Birth Certificate. Her mother gave her maiden name as her last name. So she doesn't really have her maternal or paternal last name. I'm sorry if this may come across as poorly worded, I'm just curious as to what, if anything, I can do to legally give my daughter my last name.

Changing a Child's Name: Can a Father Who Has Primary Physical Custody Change His Child's Last Name