Is it OK to refer to people like Moses Mendelson or Shabsai Tzvi by name? I have heard some call them by something else, like their initials. On the other hand is it OK to use yemach shemom after referring to them?
One should not say yemach shemo on any Jew. The Beis Yisroel (of Gur) used to say that for somebody whose death will obligated his wife in yibum, in order to preserve his name, we cannot say yemach shemo (even though the pasuk from which the words are drawn refers to Jews).
The Gemara writes that when stating the names of the wicked one must mention their doom (see Yoma 38b, and Bereishis Rabba 49), and this is why we often add the words shem reshaim yirkav after mentioning names like Shabsai Zvi.