Broadus doesn't go back to
Julius Caesar. It is an English surname, a variation of Broadhouse, originally designating someone who lived in the largest house in a medieval English village.
The use of Broadus as a given name in the Southern USA is largely because of
Baptist parents wishing to honor
John A. Broadus, a famous
Baptist preacher and author.
http://www.siteone.com/religion/baptist/baptistpage/portraits/broadus.htm
The most famous person named after
John A. Broadus was
John Broadus Watson, the founder of the Behaviorism branch of psychology.