This name was borne by four medieval rulers of Samtskhe (each from the Jaqeli dynasty), the last of whom lived in the 16th century.
In Georgian literature, Qvarqvare is the name of the eponymous character of the popular Georgian Soviet comic play Qvarqvare Tutaberi (1928) written by the Georgian playwright Polikarpe Kakabadze (1893-1972).