So what do we call these cameras?
Some of the first Internet-visible suggestions regarding removing the mirror and creating the kinds of cameras this site deals with came on the fora at DPReview. This was triggered by a post lobbying for a new kind of camera: Electronic Viewfinder Interchangeable Lens (EVIL). Obviously, EVIL isn't exactly something any respectable Japanese consumer electronics company wants to call their product, so that suggestion was pretty much kaput from the get go.
What tended to stick very early on was "mirrorless" (thus the inspiration for this Web site's name). That's because the primary change that produced different camera designs was the simple removal of the mirror, not the addition of an electronic viewfinder (EVF). That's been proven now that Sony makes a line of DSLRs that have EVFs instead of optical viewfinders: adding an EVF didn't do anything except change the nature of the mirror itself (doesn't move, partially reflecting).
Removing the mirror changed the thickness of the camera. First, the mirror was taking up room in front of the shutter (which is in front of the sensor). But since all the DSLRs were using legacy lens mounts, the lens mount itself was pushed forward of the mirror to use existing lenses. Just removing the mirror wouldn't give you a thinner camera body unless you also changed the lenses (witness the Pentax K-01). In other words, removing the mirror triggered other changes: lens mount position, lens design, use of an EVF (or at least the LCD in "live view" mode), smaller thinner body, less body area to mount controls, and so on.
Obviously, I like the mirrorless name, and mostly because it was the removal of the mirror that changed camera design and gave us all these new, interesting cameras.
The camera makers don't know what to call these things, either. When Olympus announced the E-P1, the press release contained the phrase "ultra-compact hybrid device." UCHD. No, that won't fly for marketing.
Panasonic tried a more traditional approach: "digital interchangeable lens camera" (DILC). Of course, DSLRs are, by definition, DILCs, so that won't work unless you want to convince people you're making DSLRs when you aren't (which Panasonic did).
Nikon, who had several years to try to figure out what it really wanted to call these cameras punted: "an advanced camera with interchangeable lenses." (ACIL)
Other phrases we've seen are "compact interchangeable lens cameras" (CILC), "small interchanageable lens cameras" (SILC), and "small systems cameras" (SSC). In fact, I've seen more potential generic names for these cameras than I've seen cameras! In other words, no one really knows what to call them.
I'll call them mirrorless. I suggest everyone else does, too, and we just get back to something more important to do.