Saw your photo.
I've got several of these suckers sitting right in front of me as I type, but I haven't got the slightest idea what they're called. Maybe, "CD sales presentation case." But that's too long and clumsy. "CD box" would be ok, if it were rectangular--but that may be a personal prejudice. I guess there are non-rectangular boxes--like Valentine's Day heart-shaped candy boxes. Maybe we need a word. Go for it!
Hey! After Opera and IE flatly refused to load the picture I decided to use Netscape and that one was eager to help (perhaps to give me a hint that I should use it more?).
To tell you the truth we call it "case" (I think; quite often these thingies go around with more names than an undercover agent) but I realise that could cause some confusion with the CD cases for "single" CDs.
Majlo-- I couldn't open your page, even with my high-speed connection. But we tend to call CD boxes cases, and the usual hard plastic kind that most of them come in (as opposed to an envelope or sleeve) is called a "jewel case" or a "jewelbox case."
Edit: I see you're not talking about individual cases. In that case, it's either a CD carrier or a CD album.