Yep, she's Lulu. There's a strange running gag in the play--which I considered cutting, but I'm trying to avoid doing that unless it's irrevocably dated(it won't be Jack the Ripper at the end, for instance)--that each of the men she's with renames her. In this case Goll chose "Nellie."
I don't think I can take any credit re: the writing, though as I said, I am modernizing and rephrasing almost everything in the process of adaptation(and Lulu's remark about the symbolism of the cat was my own invention), but that's Wedekind, really, not me. Well, via translation. (Christ, I wish I knew German)