On April 30, 2022, at the initiative of A. S. Agadjanian and his graduate student E. D. Protasov, an international round table “Modern Old Believership: Social and Anthropological Research” was organized at the Center for the Study of Religions at Russian State University of Humanities. The topics for discussion were recent and promising scientific research, new approaches in the study of Old Believers as a religious and cultural phenomenon, as well as various concepts concerning issues of identity, religious and social practices, discourses and texts of Old Believers. A discussion of one of the papers turned into a debate about the terminology: how to name the opponents of the church reform of the 17th century, what is the most correct way to call modern Old Believers and, accordingly, the adherents of the Russian Orthodox Church. Very interesting thoughts were expressed and then put in writing by Dr. Alexei Muravyev. Below we cite A. Muravyev’s text with the remarks of other participants in the discussion about the terms — Peter Chistyakov, Natalia Dushakova, Danila Rygovsky and Ilya Melnikov.