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-).
Although this name was used by Jews in the Middle Ages, it was not typical as an English Christian name until after the Protestant Reformation, being common among the Puritans.
This name also appears in the New Testament, belonging to man who sheltered Paul and Silas. In his case, it may represent a Hellenized form of a Hebrew name. It was not used in England until after the Protestant Reformation.