It appears to be one of the Dracaenas, and even under magnification, I can't read the name on the ticket in the pot. Some are easier than others, but all dislike direct sun, draughts, too high and top low a temperature, need to be kept reasonably moist, but not waterlogged (that is, no tray or outer pot with water left in it, this must be emptied away 30 minutes after watering), and reasonably high humidity, so not to be kept near heat sources.

I don't know how you've been keeping yours, other than the fact you've been moving it about quite a lot. It may or may not actually be dead - these plants often regenerate quite readily from the cane or main stem if given the correct conditions. Find a spot for it where its out of cold draughts, has reasonable daylight but not direct sun (particularly in summer), away from heat sources, if the soil is waterlogged, let it dry out, then water sparingly during winter, not allowing it to stand in water, and cut off the top third of each cane. Wait and see what happens - if the roots have rotted because of excessive water, though, it may well not recover.

It's a Dracaena marginata, and Bamboo's advice is spot on, though it can take a surprising amount of heat. We grow it outside in the shade, here in the desert. It looks like it succumbed to root rot, though, so I am not too hopeful. Still worth a try if the stems are still plump and firm.

You could try scratching a tiny nick on the stem. I've got mine to send out new growth that way.

I know when I've given it too much water - the leaves start to go brown. I water irregularly. It's six foot now.