Yes, its Dracaena marginata to be exact,and it needs some remedial work by the look of it. Although it tolerates low light conditions quite well, yours isn't looking too great, so if its in a really dark area, it could do with some more light.
If you're in the northern hemisphere, I'd wait till spring, then cut it down to about 6-8 inches, so you've just got the remains of two stems branching off a single one at the base. Pot up into a clean, new pot with fresh potting soil, and stand it somewhere it gets reasonable light, but not direct sunlight, water it in, and wait - it should send out new shoots from both stems. If you like, you can use the tops to start new plants; cut about 4 to 5 inches below the green topgrowth, pop the stems in a bottle of water, so the stems are immersed but the topgrowth is not, stand the bottle on a windowsill, keep it topped up,and when roots appear, pot them up separately, or choose one good one and pot that up and bin the rest if you don't want them all.
There's an image in this link of what it should look like - it's the second one down (the first image is Dracaena marginata variegata, same plant, different cultivar)