There are a host of issues associated with changing the name of a minor child. To begin with, there is no rule that says that a child must be given the father's last name. In cases where a child is born to a married couple, the parents have the right to agree on the last name of the child together; typically it is the last name of one of the parties, or a combination of the two names. Where a child is born out of wedlock, the mother has the right to decide on the last name of the child.
If a child is given one name at birth, and either the child or a parent decides that name should be changed, the court must be petitioned to hear the case. Name changes for minor children will be sent to a judge, who will use the "best interest of the child standard" when decided if the name change should be granted. Courts have explained some of the factors they take into account. These factors can include the age of the child and how the name change will affect her, the ability of the child to understand the name change, the general reason for the name change, whether the name will be changed to match other members of the household, etc.
There is no set weight given to any one factor. The court will look at the reasons for the name change over all and decide what is best for the child. For example, the court may be more inclined to change the name of a young minor child who has the biological father's last name, if the child has no relationship with the father, and has other siblings or half-siblings in the household with a different mane. A minor child also has standing to bring an action for a name change himself, and depending on the age of the child, the court may give weight to what name the child wants and why.