"I couldn't think of a more Star-Trek themed name..."
Executive Producer Bryan Fuller (who developed the concept behind the show and was slated to be its showrunner until he backed out from that role) had this to say about the naming of the ship:
BRYAN FULLER: There are so many reasons why we settled on Discovery. But the chief one amongst them was that I couldn't think of a more Star Trek-themed name for a ship than Discovery.
(Source — "Introducing the USS Discovery", Official Star Trek Web Site)
So it seems that "Discovery" captures the main themes of Star Trek, at least to Fuller. The principal mission of the principal ships in Star Trek thus far has, of course, been to discover strange new worlds and civilizations....
It's still reasonable that it might be named after the Space Shuttle Discovery, but no one has gone on record to say that. In fact, the studio has been asked the question and has avoided answering it directly:
CBS declined to comment when asked if the new ship was in fact named for the space shuttle Discovery, but released a statement from Bryan Fuller, the executive producer of Star Trek: Discovery, from his recent appearance at San Diego Comic Con.
"Discovery is so intrinsic as a concept to the philosophy of Star Trek, it felt like it was a beautiful way to acknowledge that spirit," said Fuller.