As an English name, Monica has been in general use since the 18th century. In America it reached the height of its popularity in the 1970s, declining since then. A famous bearer was the Yugoslavian tennis player Monica Seles (1973-).
Jonah's story was popular in the Middle Ages, and the Hellenized form Jonas was occasionally used in England. The form Jonah did not become common until after the Protestant Reformation.
The name was brought to England by the Normans. Notable bearers include author L. Frank Baum (1856-1919), architect Frank Lloyd Wright (1867-1959), and singer Frank Sinatra (1915-1998).