I just discovered that there is another book collection program called BookCase, available in Macintosh and Windows versions from Epigroove. That's a shame, I thought I had done a thorough search before I decided on Bookcase in the first place, the capitalization difference notwithstanding.
So I'm considering a name change. Nothing familiar or obvious springs to mind. Bookcase is not limited to books, so perhaps something hinting at media collections would be good. For kicks, I looked up the Latin word for bookcase: scrinium. One of the definitions I found was:
A receptacle in the shape of a cylinder with a removable lid, and used in ancient Rome as a container for scrolls.
There's a great list of Latin words for books and libraries at http://www.nathanielturner.com/writingbookslibraries.htm. Pegma and pluteus suggest themselves, or something iinvolving codex or colophon. Corpora? Maybe theca. These are all unfamiliar words, though, which is perhaps a drawback.
Staying with english, maybe bookchest, mediachest, or bibliophile.