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The belief you're interested in is Christian perfectionism. Perfectionism was held by a number of people during the Reformation era, and was especially widespread in the low countries. Advocates included Anabaptist Melchior Hoffman, the Reformed Sebastian Castellio, and the nondenominational Dirck Coornhert (Van Veen, 2004).
However, it's also worth considering the context for Calvinist claims of Anabaptist perfectionism. That name has been used as a derogatory epithet from the Reformation until the present.
John Calvin's own frustrations with the Anabaptists had to do with the fact that the Anabaptists "out-Calvinisted" the Reformed community on at least two important points. The first was church discipline. The Calvinists were very critical of Catholics and Lutherans for their lack of attention to the role of discipline in the Christian community. The Anabaptists, however, took discipline even further than the Calvinists, insisting on very tight patterns of communal control. The Calvinists, obviously stung by this criticism, responded by labeling the Anabaptists as "perfectionist."
-Mouw, R. J. (2000). Reflections on my encounter with the Anabaptist-Mennonite tradition. Mennonite Quarterly Review, 74(4), 571-577. summarizing Balke, 1981
As Mouw describes, Anabaptists can be understood as the extreme perfectionist end of a spectrum in terms of expectations for regeneration and personal transformation, so Berkhof may well be thinking of that spectrum without having any particular writer in mind.
While in this post I'm accepting that the label of perfectionism can be objectively applied to some writers, Perfectionism is usually a label applied by others while rejected by those to which it is applied (Augsburger, 1981).
Often those Christians and groups of Christians who have honestly and earnestly sought to live a life of high dedication, obedience, and holiness have not only been misunderstood but also frivolously condemned as hypocrites or self-righteous. The attempt to strive toward perfection ("Be ye therefore perfect even as your heavenly Father is perfect") has often been erroneously labeled perfectionism. The Anabaptists and Mennonites have suffered under this charge from the beginning.
-Harold S. Bender, Perfectionism, in Mennonite Encyclopedia.
To be thorough, you'll also want to look into early Christian debates about post-baptismal forgiveness of sins in early Christianity. Tertullian, was highly regarded among early Anabaptists, and they were surely influenced by his position.
For mainstream early Anabaptist authors perspectives on regeneration and quotes that could easily be interpreted as perfectionist, see especially Augsburger, 1981.