This one is an oddball...it's set in the near future, perhaps, but there's no real description of anything, and the first chapter pretty much explains what the rest of the novel is all about by saying that each person in this world is born nameless, and they only assume names when their lovers give them one.
Murakami ripped off a lot of this book in his `Hard boiled wonderland...' and made his name off it. The building that contains things it can't possibly contain, the name thing, the cats that talk...all written by Takahashi first. Of course, he wasn't the first ever to do it, but it really annoys when another writer gets credit for something that someone else has done better elsewhere.
Anyway, this book isn't perfect, there's nothing to really draw you in character-wise...you won't really know any of them well enough to care what happens to them, but that's kinda the point, I guess. The thing that will keep you reading is the bizarre invention on almost every page, and the short chapters that sometimes run to only a few lines.
And the gangsters, of course. They come in and out of it, but you're always wondering, what do they mean, what are they representing etc.? And, because this book is relatively unknown outside of Japan, there isn't much criticism available to explain everything to you, which means you're gonna have to figure it out for yourself. Or wait until someone else writes a book about it and tells you what to think.