A backdoor adoption is where the step parent of a child tries to avoid the legal adoption methodology by "pretending" the child is adopted.
This includes, but is not limited to, changing the child's last name to reflect the new "parents", having the child call the new parent "Daddy" or "Mommy" or other ways and types of shenanigans designed to remove the birth parents from the child's life.
These are not ways looked upon with favor in a court of law. Further, using them will almost certainly prejudice the court AGAINST the "adoptive" parents.