The name Anabaptist is derived from the Greek term anabaptista, or "one who baptizes over again." This name was given them by their enemies in reference to the practice of "re-baptizing" converts who "already had been baptized" (or sprinkled) as infants.  Anabaptists required that baptismal candidates be able to make their own confessions of faith and so rejected baptism of infants.
The early members of this movement abhorred the name "Anabaptist", claiming that since infant baptism was unscriptural and null and void, the baptizing of believers was not a "re-baptism" but in fact the first baptism for them. Balthasar Hübmaier wrote:
“I have never taught Anabaptism. ...But the right baptism of Christ, which is preceded by teaching and oral confession of faith, I teach, and say that infant baptism is a robbery of the right baptism of Christ...” 
(1) Harper, Douglas (2010) , "Anabaptist", Online Etymological Dictionary, retrieved April 25, 2011.n http://www.etymonline.com/index.php?term=Anabaptist
(2) Vedder, Henry Clay (1905). Balthasar Hübmaier, the Leader of the Anabaptists. New York: GP Putnam's Sons.