If my father has used my name without my permission, what can I do?

You need to immediately get the information to prove it and file police reports for identity theft and fraud. Contact the local police, the FBI and both the state attorney general and the U.S. Attorney. Then, contact the court agency handling the child support matters and inform the lead prosecutor regarding this matter. Most states have statutes that could haul him in to court for simply being in arrears. Pull up each of your three credit reports, and locate any transactions you do not recognize and file disputes and fraud or identity theft claims with each of those credit reporting agencies. Then, for each company, if you can locate the state in which these businesses were located, pull up the registration through the secretary of state website and print those records. Same goes for pulling up with the DMV and state registry of deeds on the cars and homes. Stay tough and keep going with the prosecutors. You may wish to consult with private counsel after you inform the state and federal agencies.