Is there a name for DSLR cameras without a viewfinder?

All DSLR’s have a viewfinder. You need it to compose your shots.

There are some small DSLR’s that do not use the traditional pentaprism and mirror arrangement.

The Panasonic L1 is one such camera The L1 flips its mirror sideways rather than upwards. This results in the L1’s viewfinder being located to the left side of the lens axis.. It also allows the L1 to feature a flat upper surface which lends it an appearance closer to a rangefinder than a DSLR.

I believe that Sony is coming out with a line of cameras like this soon. They are called EVIL which stands for something like Electronic Viewfinder something or other. To the best of my knowledge these camera will have a different mount than the Sony alpha. The alpha uses the a-mount and I believe the EVIL cameras have what is called the e-mount.

http://sonyalpharumors.com/sony-alpha-nex3-nex5/

There are also Micro-4/3rds cameras, which use a 4/3rds sensor, which is smaller than a normal DSLR sensor, but larger than a point and shoot and no mirror.

What makes an SLR (Single Lens Reflex) is the view finder. The mirror reflects the same light that the sensor sees through the view finder so that you can focus and compose your image without parallax errors if the view finder was separate. There was some advertising out in the past that suggested that an on camera LCD display made SLR view finders obsolete, but it quickly lost favor. the screen does not show enough detail especially outside under bright conditions and when taking pictures in low light, the image was worthless compared to the image seen in the viewfinder. This is why SLR cameras are coveted by professional photographers and serious amateurs.

If it does not have some mirror/viewfinder mechanism, it isn’t an SLR.

There are some excellent cameras that are not SLRs.