Audio problem: In the very first scene where we see Corso, in the high class apartment, giving his false estimate to the yuppies. He walks over to the disabled man in the wheelchair, and as he turns from the window he says "I understand." But upon closer inspection, his lips never move.
Continuity mistake: While comparing the Kessler copy with the Balkan copy, the engraving with the chess board signed with LCF is white. In order to have the devil appear in the castle, Balkan needs all 9 LCF signed engravings. When Corso appears in the tower, the engravings laid down on the table contain a black chess board. It's the one the middle, and quite distinctive. (01:23:00 - 01:53:44)
Revealing mistake: When Corso is being pushed through the floorboards (into his proper niche) we can see for a good second or two that it is certainly not Johnny Depp. (The stunt-double is Dominique Fouassier). (01:59:25)
Answer: She was not given a name, neither in the film nor credits. She is simply known as "The Girl". As to precisely who she is, it is deliberately left ambiguous. But the last engraving found by Corso does seem to indicate that she is the Whore of Babylon mentioned in the Book of Revelation.
Twotall