A well-known bearer of this name was Amasis II, an Egyptian pharaoh from the 6th century BC.
She was the daughter of Ramses II and Isetnofret, later becoming a Great Royal Wife of her father following the death of Nefertari.
Gudit was a Ethiopian falasha queen (flourished ca. 960).
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-).