Since the alphabet was conceived and popularised by the followers of Cyril and Methodius, rather than by Cyril and Methodius themselves, its name does not denote authorship, but rather homage. The name "Cyrillic" often confuses people who are not familiar with the alphabet's history, because it does not identify a country of origin (contrast with "Greek alphabet"). Some call it "Russian alphabet" because Russia is the most populous and influential user of the alphabet. Some Bulgarian intellectuals, notably Stefan Tsanev, have expressed concern over this, and have suggested that the Cyrillic alphabet be called "Bulgarian alphabet" instead, for the sake of historical accuracy.

The Cyrillic alphabet is also known as azbuka, derived from the old names of the first two letters of most variant Cyrillic alphabets.