Gillian is a name in common usage in Great Britain (where it's often pronounced with a hard "G.) but until recently had not crossed the Atlantic in significant numbers, except in the short form Jill.
In medieval England, the name Gillian was so common that it was used as a generic name for a girl, just as Jack was for a boy, hence the nursery rhyme Jack and J(G)ill and the expression "every Jack has his Jill." The high profile of actress Gillian The X Files Anderson did a lot to publicize the name in the US -- where it is more often spelled the phonetic Jillian.
Two other noteworthy bearers are Australian film director Gillian Armstrong and Gone Girl author Gillian Flynn. Gillian Boardman is a key character in Robert Heinlein's Stranger in a Strange Land.