How can I use a dresser as a room divider?

A room divider would work, even a piece of plywood. You can get two 2x2's in the height you need to go from floor to ceiling, then attach plywood to them. Cover each side to compliment the room it is facing.

You could try putting a decorative wallpaper on the back of the dresser or decoupaging it. I bet that would look great!

Cover by stapling material to match your décor and trim over the staples with braid,(this can be glued with hot melt glue).

Or back with wood strips that have been stained different shades of colour again to go with your décor.

Chalkboard paint and write an inspirational message on the back of the dresser .

How about finding a bookcase the same size or slightly bigger to put up to the back of the dresser? Or could you arrange your furniture so the couch backs up to the dresser?

Beadboard is easy to apply with either construction adhesive or small brads.

I'm wondering if it would be appropriate to turn the dresser around so that it backs up to the bed, like a footboard, with the front facing the living area you have planned. I don't know if it's feasible for the person using the bedroom/dresser to have to go around to access the dresser drawers but it's always interesting to play around with placement. You could then coordinate the back of the dresser with the bedroom area by painting it in a coordinating color, hanging pictures (or a framed mirror or some clothing pegs) on the back of the dresser and snuggling some pillows up against the back of the dresser. Then you could use the top of the dresser to for living room decor (candles, ceramics, plants, framed photos/art, etc.) and make the dresser seem more like a fancy sideboard.