Changing your name is something the United States allows, providing you with the proper procedures for changing both first and last names. Children cannot change their last name until they are of legal age, but if you have sole custody, you can change your child's name by filling out a few different papers and submitting them to the courthouse, following the proper legal channels.
File a name change petition in your state or county courthouse. These are typically available online for your convenience, or you can ask the court clerk which forms are necessary for a name change. The petition is the form that lists the pertinent information for the name change.
File an affidavit of consent. Even if you have sole custody, if the child's father has any rights to him, as granted through the courts, an affidavit of consent shows the court that he has agreed to execute a name change.
File the other documentation, as outlined in your state regulations for name changes. You may need to file a notice of petition, which informs the public about the name change through a newspaper or other public publication. If the name change is for safety reasons, you may be exempt from this requirement.
Attend a hearing in front of the judge if your state requires it. If there is no opposition and the forms are filled out completely, the judge may grant the change without any hassles. If the father does not consent, he may require a hearing to hear both sides of the story to determine whether or not the name change is warranted.