The current naming system is:
Note that the second letter is never further up the alphabet than the first, that is to say no star can be BA, CA, CB, DA or so on.
In the early 19th century few variable stars were known, so it seemed reasonable to use the letters of the Roman alphabet, starting from the letter R so as to avoid confusion with letter spectral types or the (now rarely used) Latin-letter Bayer designations. This system of astronomical naming convention was developed by Friedrich W. Argelander. There is a widespread belief according to which Argelander chose the letter R for German rot or French rouge, both meaning "red", because many variable stars known at that time appear red. However, Argelander's own statement disproves this.
By 1836, even the letter S had only been used in one constellation, Serpens. With the advent of photography the number of variables piled up quickly, and variable star names soon fell into the Bayer trap of reaching the end of the alphabet while still having stars to name. After two subsequent supplementary double-lettering systems hit similar limits, numbers were finally introduced.