legal name

I wish to run for public office without using my surname. I have signed my driver's license with first and middle name. I am filling out paperwork to run as a candidate and asked the question if I could run as "First name ,Middle name" of the family (last Name). My board of elections contacted the secretary of state with that question. They came back with the question "What is your legal name?" I know I need to change my voter registration to match what legal name I wish to run as. I have documentation (notarized) from my parents stating they named me "first name, Middle name of the family "last name". Should have this document filed with the clerk of courts in my county to establish my "legal name"? According to Black's 4th ed. your surname is part of your legal name.