New H1B stamping needed if passport name changed?


In my current passport I have only first name (Sangamesh), in my H1B stamp I have only last name(FNU, Sangamesh) and in my I797 I have both First name and last name(Sangamesh Hubballi). Now am applying for a new passport with my full name (Sangamesh Hubballi). Should I also go for visa stamping again?