OP---what you need is a separation light, often called a kicker light, behind the subject's posing line, coming in from the back and slightly off to one side. See Gary's shot of the dog portrait shoot, in Post #19? behind the posing line he has mounted a flash with a small-diameter reflector, a barn doors set, and what looks like, maybe, a mylar diffuser over the front of the reflector. This is a common way to light the edges of people in a portrait-type setting, but it works for pets also. Many people, me included, would use a honeycomb grid over the reflector on the kicker light. The mylar diffusing material is something I am very,very keen on using. I normally use a metal reflector, 20 degree grid, barn doors, and one, or two, or sometimes even three sheets of mylar diffusing material slid into the barn door set's "gel holder slot".
In a realllllllly cramped, confined space like this, light falls off **exceptionally** rapidly; the shooting area you are working on is extremely cramped, and it would be tricky for a beginning studio shooter to get even light over much distance in that room.
If you can rig up some kind of a separation/kicker light that comes in from behind and off to the side and angling downward a bit, you'll get a little "rim" of light that lights up the outline fur/body of the dark animals, and makes them look so much more three-dimensional.
When a background/separation/hair light comes in from a steep angle, like say from 10 or 11 o'clock angle, with the lens aimed from 6 o'clock to Noon in lens-axis angle, it takes very,very little light to create an outline of light that is "hot", or even "too hot"...this is why the use of a grid, and diffusers, and barn doors--as a way to control the amount and spread of the light that is coming mostly toward the camera position.
Even if you just fire a flash off of a big white board placed at 10 o'clock and behind and off to the side of the dog-posing area, you'll get some separation light that would help; the placement of the board can help keep stray light from striking the black background. A small, cheap 8x8 inch softbox and a speedlight at 1/16 power behind and at 10 o'clock might be something to look into. But you gotta get something...some way to separate the animals from that black fabric!
When working in VERY close spaces like this, the amount of light needed is very small, and the ability to control the light is really important. The shorter the distance the light travels to the subject--the MORE-variable the light's brightness is over even short differences in distance. Moving the lights farther away from the posing area creates a more-even illumination over more inches of real space.