IS IT TRUE THAT YOU CAN CHANGE YOUR NAME AND LAST NAME FOR ANY KIND OF NAME YOU CHOSE,WHEN YOU BECOME CITIZEN?

Im seperated but still married, my husband start living with a person which they have a kid together and she become citizen of usa. She chose to change her name to my husband last name without getting married, just because. I was wondering if anyone can do that without any kind of married certificate or birth certificate? EG i want to be rename myself as Elizabeth Taylor or Hilary Clinton? Its that legal?