My understanding of the traditional definition of the Ana Baptist, comes from back in the days of the Reformation.
Because the Reformers kept up the practice of baptizing infants (carried over from the RCC), the Ana-Baptists believed that one must be baptized as one who willingly and consciously made a decision out of faith, for which an infant couldn't do.
So the Ana- simply means 'again'. To be baptized again. The Ana-Baptists were persecuted harshly by both the RCC and the Protestant Reformers.
I've found numerous sources, but this is pretty simple. Can't vouche for the whole site, just this article.