I was a bit confused by this, since I usually associate "calibre" with the e-book creation/conversion software with that name.
Looks like Calibre also holds a trademark: http://tmsearch.uspto.gov/bin/showfield?f=doc&state=4806:h6j...
There seems to be a high likelihood of confusion given that both are software products, but IANAL.
My understanding is that you can have overlap in trademarked names when it's in very different markets, but IANAL
IANAL but I don't think the trademark is an issue. Might make it a bit hard to search for, though, when "calibre app" is dominated by calibre e-book software.