Sources on the meaning and origin of names seem to agree that "Gillian" is a feminine version of the name "Julian", and the G is soft. Julian is from the Latin and is pronounced with either a soft "J" or "Y", but in English this is invariably "J". This confirms that the "correct" pronunciation of Gillian is with a soft G.

However it is of course up to the individual how they choose to say their own name. I used to work with someone who pronounced his own surname in different ways, so it is quite possible that Gillian Welch uses both hard and soft G interchangeably.